jm2.25lem1 - Mathbox for Stefan O'Rear

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Theorem jm2.25lem1 37565

Description: Lemma for jm2.26 37569. (Contributed by Stefan O'Rear, 2-Oct-2014.)

**Assertion**
Ref	Expression
jm2.25lem1	$/\$ $/\$ $/\$ $/\$ $\/$ $\/$ $\/$

**Proof of Theorem jm2.25lem1**
Step	Hyp	Ref	Expression
1		simpl1l 1112	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
2		simpl2l 1114	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
3		simpl2r 1115	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
4		simpl1r 1113	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
5		simpl3 1066	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
6		simpr 477	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
7		acongtr 37545	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
8	1, 2, 3, 4, 5, 6, 7	syl222anc 1342	. 2 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
9		simpl1l 1112	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
10		simpl2r 1115	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
11		simpl2l 1114	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
12		simpl1r 1113	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$
13		simpl3 1066	. . . 4 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
14		acongsym 37543	. . . 4 $/\$ $/\$ $/\$ $\/$ $\/$
15	9, 11, 10, 13, 14	syl31anc 1329	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
16		simpr 477	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
17		acongtr 37545	. . 3 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
18	9, 10, 11, 12, 15, 16, 17	syl222anc 1342	. 2 $/\$ $/\$ $/\$ $/\$ $\/$ $/\$ $\/$ $\/$
19	8, 18	impbida 877	1 $/\$ $/\$ $/\$ $/\$ $\/$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 196 $\/$ wo 383 $/\$ wa 384 $/\$ w3a 1037

wcel 1990 class class class wbr 4653 (class class class)co 6650

cmin 10266

cneg 10267

cz 11377

cdvds 14983

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-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 ax-pre-ltadd 10012 ax-pre-mulgt0 10013

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-nel 2898 df-ral 2917 df-rex 2918 df-reu 2919 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-iun 4522 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-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-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-om 7066 df-wrecs 7407 df-recs 7468 df-rdg 7506 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-xr 10078 df-ltxr 10079 df-le 10080 df-sub 10268 df-neg 10269 df-nn 11021 df-n0 11293 df-z 11378 df-dvds 14984

This theorem is referenced by: jm2.25 37566