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Mirrors > Home > MPE Home > Th. List > Mathboxes > fmtno5faclem3 | Structured version Visualization version Unicode version |
Description: Lemma 3 for fmtno5fac 41494. (Contributed by AV, 22-Jul-2021.) |
Ref | Expression |
---|---|
fmtno5faclem3 | ;;;;;;;; ;;;;;;; ;;;;;;;; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4nn0 11311 | . . . . . . . . 9 | |
2 | 0nn0 11307 | . . . . . . . . 9 | |
3 | 1, 2 | deccl 11512 | . . . . . . . 8 ; |
4 | 2nn0 11309 | . . . . . . . 8 | |
5 | 3, 4 | deccl 11512 | . . . . . . 7 ;; |
6 | 5, 2 | deccl 11512 | . . . . . 6 ;;; |
7 | 6, 4 | deccl 11512 | . . . . 5 ;;;; |
8 | 5nn0 11312 | . . . . 5 | |
9 | 7, 8 | deccl 11512 | . . . 4 ;;;;; |
10 | 9, 2 | deccl 11512 | . . 3 ;;;;;; |
11 | 10, 4 | deccl 11512 | . 2 ;;;;;;; |
12 | 6nn0 11313 | . . . . . . . 8 | |
13 | 4, 12 | deccl 11512 | . . . . . . 7 ; |
14 | 8nn0 11315 | . . . . . . 7 | |
15 | 13, 14 | deccl 11512 | . . . . . 6 ;; |
16 | 15, 2 | deccl 11512 | . . . . 5 ;;; |
17 | 1nn0 11308 | . . . . 5 | |
18 | 16, 17 | deccl 11512 | . . . 4 ;;;; |
19 | 18, 12 | deccl 11512 | . . 3 ;;;;; |
20 | 19, 12 | deccl 11512 | . 2 ;;;;;; |
21 | eqid 2622 | . 2 ;;;;;;;; ;;;;;;;; | |
22 | eqid 2622 | . 2 ;;;;;;; ;;;;;;; | |
23 | eqid 2622 | . . 3 ;;;;;;; ;;;;;;; | |
24 | eqid 2622 | . . 3 ;;;;;; ;;;;;; | |
25 | eqid 2622 | . . . 4 ;;;;;; ;;;;;; | |
26 | eqid 2622 | . . . 4 ;;;;; ;;;;; | |
27 | eqid 2622 | . . . . 5 ;;;;; ;;;;; | |
28 | eqid 2622 | . . . . 5 ;;;; ;;;; | |
29 | eqid 2622 | . . . . . 6 ;;;; ;;;; | |
30 | eqid 2622 | . . . . . 6 ;;; ;;; | |
31 | eqid 2622 | . . . . . . 7 ;;; ;;; | |
32 | eqid 2622 | . . . . . . 7 ;; ;; | |
33 | eqid 2622 | . . . . . . . 8 ;; ;; | |
34 | eqid 2622 | . . . . . . . 8 ; ; | |
35 | eqid 2622 | . . . . . . . . 9 ; ; | |
36 | 2cn 11091 | . . . . . . . . . 10 | |
37 | 36 | addid2i 10224 | . . . . . . . . 9 |
38 | 1, 2, 4, 35, 37 | decaddi 11579 | . . . . . . . 8 ; ; |
39 | 6cn 11102 | . . . . . . . . 9 | |
40 | 6p2e8 11169 | . . . . . . . . 9 | |
41 | 39, 36, 40 | addcomli 10228 | . . . . . . . 8 |
42 | 3, 4, 4, 12, 33, 34, 38, 41 | decadd 11570 | . . . . . . 7 ;; ; ;; |
43 | 8cn 11106 | . . . . . . . 8 | |
44 | 43 | addid2i 10224 | . . . . . . 7 |
45 | 5, 2, 13, 14, 31, 32, 42, 44 | decadd 11570 | . . . . . 6 ;;; ;; ;;; |
46 | 36 | addid1i 10223 | . . . . . 6 |
47 | 6, 4, 15, 2, 29, 30, 45, 46 | decadd 11570 | . . . . 5 ;;;; ;;; ;;;; |
48 | 5p1e6 11155 | . . . . 5 | |
49 | 7, 8, 16, 17, 27, 28, 47, 48 | decadd 11570 | . . . 4 ;;;;; ;;;; ;;;;; |
50 | 39 | addid2i 10224 | . . . 4 |
51 | 9, 2, 18, 12, 25, 26, 49, 50 | decadd 11570 | . . 3 ;;;;;; ;;;;; ;;;;;; |
52 | 10, 4, 19, 12, 23, 24, 51, 41 | decadd 11570 | . 2 ;;;;;;; ;;;;;; ;;;;;;; |
53 | 11, 2, 20, 14, 21, 22, 52, 44 | decadd 11570 | 1 ;;;;;;;; ;;;;;;; ;;;;;;;; |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 (class class class)co 6650 cc0 9936 c1 9937 caddc 9939 c2 11070 c4 11072 c5 11073 c6 11074 c8 11076 ;cdc 11493 |
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 |
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-ov 6653 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-ltxr 10079 df-nn 11021 df-2 11079 df-3 11080 df-4 11081 df-5 11082 df-6 11083 df-7 11084 df-8 11085 df-9 11086 df-n0 11293 df-dec 11494 |
This theorem is referenced by: fmtno5fac 41494 |
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