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Mirrors > Home > ILE Home > Th. List > findcard2d | Unicode version |
Description: Deduction version of findcard2 6783. If you also need (which doesn't come for free due to ssfiexmid 6770), use findcard2sd 6786 instead. (Contributed by SO, 16-Jul-2018.) |
Ref | Expression |
---|---|
findcard2d.ch | |
findcard2d.th | |
findcard2d.ta | |
findcard2d.et | |
findcard2d.z | |
findcard2d.i | |
findcard2d.a |
Ref | Expression |
---|---|
findcard2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3117 | . 2 | |
2 | findcard2d.a | . . . 4 | |
3 | 2 | adantr 274 | . . 3 |
4 | sseq1 3120 | . . . . . 6 | |
5 | 4 | anbi2d 459 | . . . . 5 |
6 | findcard2d.ch | . . . . 5 | |
7 | 5, 6 | imbi12d 233 | . . . 4 |
8 | sseq1 3120 | . . . . . 6 | |
9 | 8 | anbi2d 459 | . . . . 5 |
10 | findcard2d.th | . . . . 5 | |
11 | 9, 10 | imbi12d 233 | . . . 4 |
12 | sseq1 3120 | . . . . . 6 | |
13 | 12 | anbi2d 459 | . . . . 5 |
14 | findcard2d.ta | . . . . 5 | |
15 | 13, 14 | imbi12d 233 | . . . 4 |
16 | sseq1 3120 | . . . . . 6 | |
17 | 16 | anbi2d 459 | . . . . 5 |
18 | findcard2d.et | . . . . 5 | |
19 | 17, 18 | imbi12d 233 | . . . 4 |
20 | findcard2d.z | . . . . 5 | |
21 | 20 | adantr 274 | . . . 4 |
22 | simprl 520 | . . . . . . . 8 | |
23 | simprr 521 | . . . . . . . . 9 | |
24 | 23 | unssad 3253 | . . . . . . . 8 |
25 | 22, 24 | jca 304 | . . . . . . 7 |
26 | id 19 | . . . . . . . . . . 11 | |
27 | vsnid 3557 | . . . . . . . . . . . 12 | |
28 | elun2 3244 | . . . . . . . . . . . 12 | |
29 | 27, 28 | mp1i 10 | . . . . . . . . . . 11 |
30 | 26, 29 | sseldd 3098 | . . . . . . . . . 10 |
31 | 30 | ad2antll 482 | . . . . . . . . 9 |
32 | simplr 519 | . . . . . . . . 9 | |
33 | 31, 32 | eldifd 3081 | . . . . . . . 8 |
34 | findcard2d.i | . . . . . . . 8 | |
35 | 22, 24, 33, 34 | syl12anc 1214 | . . . . . . 7 |
36 | 25, 35 | embantd 56 | . . . . . 6 |
37 | 36 | ex 114 | . . . . 5 |
38 | 37 | com23 78 | . . . 4 |
39 | 7, 11, 15, 19, 21, 38 | findcard2s 6784 | . . 3 |
40 | 3, 39 | mpcom 36 | . 2 |
41 | 1, 40 | mpan2 421 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cdif 3068 cun 3069 wss 3071 c0 3363 csn 3527 cfn 6634 |
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-coll 4043 ax-sep 4046 ax-nul 4054 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 ax-iinf 4502 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-3or 963 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-ne 2309 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-if 3475 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-tr 4027 df-id 4215 df-iord 4288 df-on 4290 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-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-er 6429 df-en 6635 df-fin 6637 |
This theorem is referenced by: iunfidisj 6834 |
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