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Mirrors > Home > ILE Home > Th. List > fidcenumlemrk | Unicode version |
Description: Lemma for fidcenum 6913. (Contributed by Jim Kingdon, 20-Oct-2022.) |
Ref | Expression |
---|---|
fidcenumlemr.dc | DECID |
fidcenumlemr.f | |
fidcenumlemrk.k | |
fidcenumlemrk.kn | |
fidcenumlemrk.x |
Ref | Expression |
---|---|
fidcenumlemrk |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fidcenumlemrk.k | . 2 | |
2 | fidcenumlemrk.kn | . . 3 | |
3 | 2 | ancli 321 | . 2 |
4 | sseq1 3161 | . . . . 5 | |
5 | 4 | anbi2d 460 | . . . 4 |
6 | imaeq2 4937 | . . . . . 6 | |
7 | 6 | eleq2d 2234 | . . . . 5 |
8 | 7 | notbid 657 | . . . . 5 |
9 | 7, 8 | orbi12d 783 | . . . 4 |
10 | 5, 9 | imbi12d 233 | . . 3 |
11 | sseq1 3161 | . . . . 5 | |
12 | 11 | anbi2d 460 | . . . 4 |
13 | imaeq2 4937 | . . . . . 6 | |
14 | 13 | eleq2d 2234 | . . . . 5 |
15 | 14 | notbid 657 | . . . . 5 |
16 | 14, 15 | orbi12d 783 | . . . 4 |
17 | 12, 16 | imbi12d 233 | . . 3 |
18 | sseq1 3161 | . . . . 5 | |
19 | 18 | anbi2d 460 | . . . 4 |
20 | imaeq2 4937 | . . . . . 6 | |
21 | 20 | eleq2d 2234 | . . . . 5 |
22 | 21 | notbid 657 | . . . . 5 |
23 | 21, 22 | orbi12d 783 | . . . 4 |
24 | 19, 23 | imbi12d 233 | . . 3 |
25 | sseq1 3161 | . . . . 5 | |
26 | 25 | anbi2d 460 | . . . 4 |
27 | imaeq2 4937 | . . . . . 6 | |
28 | 27 | eleq2d 2234 | . . . . 5 |
29 | 28 | notbid 657 | . . . . 5 |
30 | 28, 29 | orbi12d 783 | . . . 4 |
31 | 26, 30 | imbi12d 233 | . . 3 |
32 | noel 3409 | . . . . . 6 | |
33 | ima0 4958 | . . . . . . 7 | |
34 | 33 | eleq2i 2231 | . . . . . 6 |
35 | 32, 34 | mtbir 661 | . . . . 5 |
36 | 35 | a1i 9 | . . . 4 |
37 | 36 | olcd 724 | . . 3 |
38 | fidcenumlemr.dc | . . . . . 6 DECID | |
39 | 38 | ad2antrl 482 | . . . . 5 DECID |
40 | fidcenumlemr.f | . . . . . 6 | |
41 | 40 | ad2antrl 482 | . . . . 5 |
42 | simpll 519 | . . . . 5 | |
43 | simprr 522 | . . . . 5 | |
44 | simprl 521 | . . . . . 6 | |
45 | sssucid 4388 | . . . . . . 7 | |
46 | 45, 43 | sstrid 3149 | . . . . . 6 |
47 | simplr 520 | . . . . . 6 | |
48 | 44, 46, 47 | mp2and 430 | . . . . 5 |
49 | fidcenumlemrk.x | . . . . . 6 | |
50 | 49 | ad2antrl 482 | . . . . 5 |
51 | 39, 41, 42, 43, 48, 50 | fidcenumlemrks 6910 | . . . 4 |
52 | 51 | exp31 362 | . . 3 |
53 | 10, 17, 24, 31, 37, 52 | finds 4572 | . 2 |
54 | 1, 3, 53 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 698 DECID wdc 824 wceq 1342 wcel 2135 wral 2442 wss 3112 c0 3405 csuc 4338 com 4562 cima 4602 wfo 5181 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-nul 4103 ax-pow 4148 ax-pr 4182 ax-un 4406 ax-iinf 4560 |
This theorem depends on definitions: df-bi 116 df-dc 825 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-sbc 2948 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-nul 3406 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-int 3820 df-br 3978 df-opab 4039 df-id 4266 df-suc 4344 df-iom 4563 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-rn 4610 df-res 4611 df-ima 4612 df-iota 5148 df-fun 5185 df-fn 5186 df-f 5187 df-fo 5189 df-fv 5191 |
This theorem is referenced by: fidcenumlemr 6912 ennnfonelemdc 12295 |
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