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Mirrors > Home > ILE Home > Th. List > fidcenumlemrk | Unicode version |
Description: Lemma for fidcenum 6844. (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 3120 | . . . . 5 | |
5 | 4 | anbi2d 459 | . . . 4 |
6 | imaeq2 4877 | . . . . . 6 | |
7 | 6 | eleq2d 2209 | . . . . 5 |
8 | 7 | notbid 656 | . . . . 5 |
9 | 7, 8 | orbi12d 782 | . . . 4 |
10 | 5, 9 | imbi12d 233 | . . 3 |
11 | sseq1 3120 | . . . . 5 | |
12 | 11 | anbi2d 459 | . . . 4 |
13 | imaeq2 4877 | . . . . . 6 | |
14 | 13 | eleq2d 2209 | . . . . 5 |
15 | 14 | notbid 656 | . . . . 5 |
16 | 14, 15 | orbi12d 782 | . . . 4 |
17 | 12, 16 | imbi12d 233 | . . 3 |
18 | sseq1 3120 | . . . . 5 | |
19 | 18 | anbi2d 459 | . . . 4 |
20 | imaeq2 4877 | . . . . . 6 | |
21 | 20 | eleq2d 2209 | . . . . 5 |
22 | 21 | notbid 656 | . . . . 5 |
23 | 21, 22 | orbi12d 782 | . . . 4 |
24 | 19, 23 | imbi12d 233 | . . 3 |
25 | sseq1 3120 | . . . . 5 | |
26 | 25 | anbi2d 459 | . . . 4 |
27 | imaeq2 4877 | . . . . . 6 | |
28 | 27 | eleq2d 2209 | . . . . 5 |
29 | 28 | notbid 656 | . . . . 5 |
30 | 28, 29 | orbi12d 782 | . . . 4 |
31 | 26, 30 | imbi12d 233 | . . 3 |
32 | noel 3367 | . . . . . 6 | |
33 | ima0 4898 | . . . . . . 7 | |
34 | 33 | eleq2i 2206 | . . . . . 6 |
35 | 32, 34 | mtbir 660 | . . . . 5 |
36 | 35 | a1i 9 | . . . 4 |
37 | 36 | olcd 723 | . . 3 |
38 | fidcenumlemr.dc | . . . . . 6 DECID | |
39 | 38 | ad2antrl 481 | . . . . 5 DECID |
40 | fidcenumlemr.f | . . . . . 6 | |
41 | 40 | ad2antrl 481 | . . . . 5 |
42 | simpll 518 | . . . . 5 | |
43 | simprr 521 | . . . . 5 | |
44 | simprl 520 | . . . . . 6 | |
45 | sssucid 4337 | . . . . . . 7 | |
46 | 45, 43 | sstrid 3108 | . . . . . 6 |
47 | simplr 519 | . . . . . 6 | |
48 | 44, 46, 47 | mp2and 429 | . . . . 5 |
49 | fidcenumlemrk.x | . . . . . 6 | |
50 | 49 | ad2antrl 481 | . . . . 5 |
51 | 39, 41, 42, 43, 48, 50 | fidcenumlemrks 6841 | . . . 4 |
52 | 51 | exp31 361 | . . 3 |
53 | 10, 17, 24, 31, 37, 52 | finds 4514 | . 2 |
54 | 1, 3, 53 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 697 DECID wdc 819 wceq 1331 wcel 1480 wral 2416 wss 3071 c0 3363 csuc 4287 com 4504 cima 4542 wfo 5121 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-nul 4054 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-iinf 4502 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-br 3930 df-opab 3990 df-id 4215 df-suc 4293 df-iom 4505 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-fo 5129 df-fv 5131 |
This theorem is referenced by: fidcenumlemr 6843 ennnfonelemdc 11912 |
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