Theorem tskcard 9603

Description: An even more direct relationship than r1tskina 9604 to get an inaccessible cardinal out of a Tarski class: the size of any nonempty Tarski class is an inaccessible cardinal. (Contributed by Mario Carneiro, 9-Jun-2013.)

Assertion

Ref	Expression
tskcard	|- ( ( T e. Tarski /\ T =/= (/) ) -> ( card ` T ) e. Inacc )

Proof of Theorem tskcard

Dummy variables w x y z are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		cardeq0 9374	. . . 4 |- ( T e. Tarski -> ( ( card ` T ) = (/) <-> T = (/) ) )
2	1	necon3bid 2838	. . 3 |- ( T e. Tarski -> ( ( card ` T ) =/= (/) <-> T =/= (/) ) )
3	2	biimpar 502	. 2 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( card ` T ) =/= (/) )
4		eqid 2622	. . . . . 6 |- ( z e. ( cf ` ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ) |-> (har ` ( w ` z ) ) ) = ( z e. ( cf ` ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ) |-> (har ` ( w ` z ) ) )
5	4	pwcfsdom 9405	. . . . 5 |- ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ~< ( ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ^m ( cf ` ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ) )
6		vpwex 4849	. . . . . . . . . . . 12 |- ~P x e. _V
7	6	canth2 8113	. . . . . . . . . . 11 |- ~P x ~< ~P ~P x
8		simpl 473	. . . . . . . . . . . . 13 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> T e. Tarski )
9		cardon 8770	. . . . . . . . . . . . . . . . 17 |- ( card ` T ) e. On
10	9	oneli 5835	. . . . . . . . . . . . . . . 16 |- ( x e. ( card ` T ) -> x e. On )
11	10	adantl 482	. . . . . . . . . . . . . . 15 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> x e. On )
12		cardsdomelir 8799	. . . . . . . . . . . . . . . 16 |- ( x e. ( card ` T ) -> x ~< T )
13	12	adantl 482	. . . . . . . . . . . . . . 15 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> x ~< T )
14		tskord 9602	. . . . . . . . . . . . . . 15 |- ( ( T e. Tarski /\ x e. On /\ x ~< T ) -> x e. T )
15	8, 11, 13, 14	syl3anc 1326	. . . . . . . . . . . . . 14 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> x e. T )
16		tskpw 9575	. . . . . . . . . . . . . . 15 |- ( ( T e. Tarski /\ x e. T ) -> ~P x e. T )
17		tskpwss 9574	. . . . . . . . . . . . . . 15 |- ( ( T e. Tarski /\ ~P x e. T ) -> ~P ~P x C_ T )
18	16, 17	syldan 487	. . . . . . . . . . . . . 14 |- ( ( T e. Tarski /\ x e. T ) -> ~P ~P x C_ T )
19	15, 18	syldan 487	. . . . . . . . . . . . 13 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> ~P ~P x C_ T )
20		ssdomg 8001	. . . . . . . . . . . . 13 |- ( T e. Tarski -> ( ~P ~P x C_ T -> ~P ~P x ~<_ T ) )
21	8, 19, 20	sylc 65	. . . . . . . . . . . 12 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> ~P ~P x ~<_ T )
22		cardidg 9370	. . . . . . . . . . . . . 14 |- ( T e. Tarski -> ( card ` T ) ~~ T )
23	22	ensymd 8007	. . . . . . . . . . . . 13 |- ( T e. Tarski -> T ~~ ( card ` T ) )
24	23	adantr 481	. . . . . . . . . . . 12 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> T ~~ ( card ` T ) )
25		domentr 8015	. . . . . . . . . . . 12 |- ( ( ~P ~P x ~<_ T /\ T ~~ ( card ` T ) ) -> ~P ~P x ~<_ ( card ` T ) )
26	21, 24, 25	syl2anc 693	. . . . . . . . . . 11 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> ~P ~P x ~<_ ( card ` T ) )
27		sdomdomtr 8093	. . . . . . . . . . 11 |- ( ( ~P x ~< ~P ~P x /\ ~P ~P x ~<_ ( card ` T ) ) -> ~P x ~< ( card ` T ) )
28	7, 26, 27	sylancr 695	. . . . . . . . . 10 |- ( ( T e. Tarski /\ x e. ( card ` T ) ) -> ~P x ~< ( card ` T ) )
29	28	ralrimiva 2966	. . . . . . . . 9 |- ( T e. Tarski -> A. x e. ( card ` T ) ~P x ~< ( card ` T ) )
30	29	adantr 481	. . . . . . . 8 |- ( ( T e. Tarski /\ T =/= (/) ) -> A. x e. ( card ` T ) ~P x ~< ( card ` T ) )
31		inawinalem 9511	. . . . . . . . . 10 |- ( ( card ` T ) e. On -> ( A. x e. ( card ` T ) ~P x ~< ( card ` T ) -> A. x e. ( card ` T ) E. y e. ( card ` T ) x ~< y ) )
32	9, 31	ax-mp 5	. . . . . . . . 9 |- ( A. x e. ( card ` T ) ~P x ~< ( card ` T ) -> A. x e. ( card ` T ) E. y e. ( card ` T ) x ~< y )
33		winainflem 9515	. . . . . . . . . 10 |- ( ( ( card ` T ) =/= (/) /\ ( card ` T ) e. On /\ A. x e. ( card ` T ) E. y e. ( card ` T ) x ~< y ) -> om C_ ( card ` T ) )
34	9, 33	mp3an2 1412	. . . . . . . . 9 |- ( ( ( card ` T ) =/= (/) /\ A. x e. ( card ` T ) E. y e. ( card ` T ) x ~< y ) -> om C_ ( card ` T ) )
35	32, 34	sylan2 491	. . . . . . . 8 |- ( ( ( card ` T ) =/= (/) /\ A. x e. ( card ` T ) ~P x ~< ( card ` T ) ) -> om C_ ( card ` T ) )
36	3, 30, 35	syl2anc 693	. . . . . . 7 |- ( ( T e. Tarski /\ T =/= (/) ) -> om C_ ( card ` T ) )
37		cardidm 8785	. . . . . . 7 |- ( card ` ( card ` T ) ) = ( card ` T )
38		cardaleph 8912	. . . . . . 7 |- ( ( om C_ ( card ` T ) /\ ( card ` ( card ` T ) ) = ( card ` T ) ) -> ( card ` T ) = ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) )
39	36, 37, 38	sylancl 694	. . . . . 6 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( card ` T ) = ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) )
40	39	fveq2d 6195	. . . . . . 7 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( cf ` ( card ` T ) ) = ( cf ` ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ) )
41	39, 40	oveq12d 6668	. . . . . 6 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) = ( ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ^m ( cf ` ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ) ) )
42	39, 41	breq12d 4666	. . . . 5 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( ( card ` T ) ~< ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) <-> ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ~< ( ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ^m ( cf ` ( aleph ` |^| { x e. On | ( card ` T ) C_ ( aleph ` x ) } ) ) ) ) )
43	5, 42	mpbiri 248	. . . 4 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( card ` T ) ~< ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) )
44		simp1 1061	. . . . . . . . . . . 12 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) /\ x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) -> T e. Tarski )
45		simp3 1063	. . . . . . . . . . . . 13 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) /\ x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) -> x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) )
46		fvex 6201	. . . . . . . . . . . . . . . 16 |- ( card ` T ) e. _V
47		fvex 6201	. . . . . . . . . . . . . . . 16 |- ( cf ` ( card ` T ) ) e. _V
48	46, 47	elmap 7886	. . . . . . . . . . . . . . 15 |- ( x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) <-> x : ( cf ` ( card ` T ) ) --> ( card ` T ) )
49		fssxp 6060	. . . . . . . . . . . . . . 15 |- ( x : ( cf ` ( card ` T ) ) --> ( card ` T ) -> x C_ ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) )
50	48, 49	sylbi 207	. . . . . . . . . . . . . 14 |- ( x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) -> x C_ ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) )
51	15	ex 450	. . . . . . . . . . . . . . . 16 |- ( T e. Tarski -> ( x e. ( card ` T ) -> x e. T ) )
52	51	ssrdv 3609	. . . . . . . . . . . . . . 15 |- ( T e. Tarski -> ( card ` T ) C_ T )
53		cfle 9076	. . . . . . . . . . . . . . . . 17 |- ( cf ` ( card ` T ) ) C_ ( card ` T )
54		sstr 3611	. . . . . . . . . . . . . . . . 17 |- ( ( ( cf ` ( card ` T ) ) C_ ( card ` T ) /\ ( card ` T ) C_ T ) -> ( cf ` ( card ` T ) ) C_ T )
55	53, 54	mpan 706	. . . . . . . . . . . . . . . 16 |- ( ( card ` T ) C_ T -> ( cf ` ( card ` T ) ) C_ T )
56		tskxpss 9594	. . . . . . . . . . . . . . . . . 18 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) C_ T /\ ( card ` T ) C_ T ) -> ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) C_ T )
57	56	3exp 1264	. . . . . . . . . . . . . . . . 17 |- ( T e. Tarski -> ( ( cf ` ( card ` T ) ) C_ T -> ( ( card ` T ) C_ T -> ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) C_ T ) ) )
58	57	com23 86	. . . . . . . . . . . . . . . 16 |- ( T e. Tarski -> ( ( card ` T ) C_ T -> ( ( cf ` ( card ` T ) ) C_ T -> ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) C_ T ) ) )
59	55, 58	mpdi 45	. . . . . . . . . . . . . . 15 |- ( T e. Tarski -> ( ( card ` T ) C_ T -> ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) C_ T ) )
60	52, 59	mpd 15	. . . . . . . . . . . . . 14 |- ( T e. Tarski -> ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) C_ T )
61		sstr2 3610	. . . . . . . . . . . . . 14 |- ( x C_ ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) -> ( ( ( cf ` ( card ` T ) ) X. ( card ` T ) ) C_ T -> x C_ T ) )
62	50, 60, 61	syl2im 40	. . . . . . . . . . . . 13 |- ( x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) -> ( T e. Tarski -> x C_ T ) )
63	45, 44, 62	sylc 65	. . . . . . . . . . . 12 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) /\ x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) -> x C_ T )
64		simp2 1062	. . . . . . . . . . . . 13 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) /\ x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) -> ( cf ` ( card ` T ) ) e. ( card ` T ) )
65		ffn 6045	. . . . . . . . . . . . . . . . 17 |- ( x : ( cf ` ( card ` T ) ) --> ( card ` T ) -> x Fn ( cf ` ( card ` T ) ) )
66		fndmeng 8034	. . . . . . . . . . . . . . . . 17 |- ( ( x Fn ( cf ` ( card ` T ) ) /\ ( cf ` ( card ` T ) ) e. _V ) -> ( cf ` ( card ` T ) ) ~~ x )
67	65, 47, 66	sylancl 694	. . . . . . . . . . . . . . . 16 |- ( x : ( cf ` ( card ` T ) ) --> ( card ` T ) -> ( cf ` ( card ` T ) ) ~~ x )
68	48, 67	sylbi 207	. . . . . . . . . . . . . . 15 |- ( x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) -> ( cf ` ( card ` T ) ) ~~ x )
69	68	ensymd 8007	. . . . . . . . . . . . . 14 |- ( x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) -> x ~~ ( cf ` ( card ` T ) ) )
70		cardsdomelir 8799	. . . . . . . . . . . . . 14 |- ( ( cf ` ( card ` T ) ) e. ( card ` T ) -> ( cf ` ( card ` T ) ) ~< T )
71		ensdomtr 8096	. . . . . . . . . . . . . 14 |- ( ( x ~~ ( cf ` ( card ` T ) ) /\ ( cf ` ( card ` T ) ) ~< T ) -> x ~< T )
72	69, 70, 71	syl2an 494	. . . . . . . . . . . . 13 |- ( ( x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) /\ ( cf ` ( card ` T ) ) e. ( card ` T ) ) -> x ~< T )
73	45, 64, 72	syl2anc 693	. . . . . . . . . . . 12 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) /\ x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) -> x ~< T )
74		tskssel 9579	. . . . . . . . . . . 12 |- ( ( T e. Tarski /\ x C_ T /\ x ~< T ) -> x e. T )
75	44, 63, 73, 74	syl3anc 1326	. . . . . . . . . . 11 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) /\ x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) -> x e. T )
76	75	3expia 1267	. . . . . . . . . 10 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) ) -> ( x e. ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) -> x e. T ) )
77	76	ssrdv 3609	. . . . . . . . 9 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) ) -> ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) C_ T )
78		ssdomg 8001	. . . . . . . . . 10 |- ( T e. Tarski -> ( ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) C_ T -> ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ~<_ T ) )
79	78	imp 445	. . . . . . . . 9 |- ( ( T e. Tarski /\ ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) C_ T ) -> ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ~<_ T )
80	77, 79	syldan 487	. . . . . . . 8 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) ) -> ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ~<_ T )
81	23	adantr 481	. . . . . . . 8 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) ) -> T ~~ ( card ` T ) )
82		domentr 8015	. . . . . . . 8 |- ( ( ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ~<_ T /\ T ~~ ( card ` T ) ) -> ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ~<_ ( card ` T ) )
83	80, 81, 82	syl2anc 693	. . . . . . 7 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) ) -> ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ~<_ ( card ` T ) )
84		domnsym 8086	. . . . . . 7 |- ( ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ~<_ ( card ` T ) -> -. ( card ` T ) ~< ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) )
85	83, 84	syl 17	. . . . . 6 |- ( ( T e. Tarski /\ ( cf ` ( card ` T ) ) e. ( card ` T ) ) -> -. ( card ` T ) ~< ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) )
86	85	ex 450	. . . . 5 |- ( T e. Tarski -> ( ( cf ` ( card ` T ) ) e. ( card ` T ) -> -. ( card ` T ) ~< ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) )
87	86	adantr 481	. . . 4 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( ( cf ` ( card ` T ) ) e. ( card ` T ) -> -. ( card ` T ) ~< ( ( card ` T ) ^m ( cf ` ( card ` T ) ) ) ) )
88	43, 87	mt2d 131	. . 3 |- ( ( T e. Tarski /\ T =/= (/) ) -> -. ( cf ` ( card ` T ) ) e. ( card ` T ) )
89		cfon 9077	. . . . . 6 |- ( cf ` ( card ` T ) ) e. On
90	89, 9	onsseli 5842	. . . . 5 |- ( ( cf ` ( card ` T ) ) C_ ( card ` T ) <-> ( ( cf ` ( card ` T ) ) e. ( card ` T ) \/ ( cf ` ( card ` T ) ) = ( card ` T ) ) )
91	53, 90	mpbi 220	. . . 4 |- ( ( cf ` ( card ` T ) ) e. ( card ` T ) \/ ( cf ` ( card ` T ) ) = ( card ` T ) )
92	91	ori 390	. . 3 |- ( -. ( cf ` ( card ` T ) ) e. ( card ` T ) -> ( cf ` ( card ` T ) ) = ( card ` T ) )
93	88, 92	syl 17	. 2 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( cf ` ( card ` T ) ) = ( card ` T ) )
94		elina 9509	. 2 |- ( ( card ` T ) e. Inacc <-> ( ( card ` T ) =/= (/) /\ ( cf ` ( card ` T ) ) = ( card ` T ) /\ A. x e. ( card ` T ) ~P x ~< ( card ` T ) ) )
95	3, 93, 30, 94	syl3anbrc 1246	1 |- ( ( T e. Tarski /\ T =/= (/) ) -> ( card ` T ) e. Inacc )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384   /\ w3a 1037   = wceq 1483   e. wcel 1990   =/= wne 2794   A.wral 2912   E.wrex 2913   {crab 2916   _Vcvv 3200   C_ wss 3574   (/)c0 3915   ~Pcpw 4158   |^|cint 4475   class class class wbr 4653   |-> cmpt 4729   X. cxp 5112   Oncon0 5723   Fn wfn 5883   -->wf 5884   ` cfv 5888  (class class class)co 6650   omcom 7065   ^m cmap 7857   ~~ cen 7952   ~<_ cdom 7953   ~< csdm 7954  harchar 8461   cardccrd 8761   alephcale 8762   cfccf 8763   Inacccina 9505   Tarskictsk 9570

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-rep 4771  ax-sep 4781  ax-nul 4789  ax-pow 4843  ax-pr 4906  ax-un 6949  ax-inf2 8538  ax-ac2 9285

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1038  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-mo 2475  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-ral 2917  df-rex 2918  df-reu 2919  df-rmo 2920  df-rab 2921  df-v 3202  df-sbc 3436  df-csb 3534  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-pss 3590  df-nul 3916  df-if 4087  df-pw 4160  df-sn 4178  df-pr 4180  df-tp 4182  df-op 4184  df-uni 4437  df-int 4476  df-iun 4522  df-iin 4523  df-br 4654  df-opab 4713  df-mpt 4730  df-tr 4753  df-id 5024  df-eprel 5029  df-po 5035  df-so 5036  df-fr 5073  df-se 5074  df-we 5075  df-xp 5120  df-rel 5121  df-cnv 5122  df-co 5123  df-dm 5124  df-rn 5125  df-res 5126  df-ima 5127  df-pred 5680  df-ord 5726  df-on 5727  df-lim 5728  df-suc 5729  df-iota 5851  df-fun 5890  df-fn 5891  df-f 5892  df-f1 5893  df-fo 5894  df-f1o 5895  df-fv 5896  df-isom 5897  df-riota 6611  df-ov 6653  df-oprab 6654  df-mpt2 6655  df-om 7066  df-1st 7168  df-2nd 7169  df-wrecs 7407  df-smo 7443  df-recs 7468  df-rdg 7506  df-1o 7560  df-2o 7561  df-oadd 7564  df-er 7742  df-map 7859  df-ixp 7909  df-en 7956  df-dom 7957  df-sdom 7958  df-fin 7959  df-oi 8415  df-har 8463  df-r1 8627  df-card 8765  df-aleph 8766  df-cf 8767  df-acn 8768  df-ac 8939  df-ina 9507  df-tsk 9571

This theorem is referenced by:  r1tskina  9604  tskuni  9605  inaprc  9658