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Mirrors > Home > ILE Home > Th. List > findcard2d | Unicode version |
Description: Deduction version of findcard2 6373. If you also need (which doesn't come for free due to ssfiexmid 6361), use findcard2sd 6376 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 3018 | . 2 | |
2 | findcard2d.a | . . . 4 | |
3 | 2 | adantr 270 | . . 3 |
4 | sseq1 3020 | . . . . . 6 | |
5 | 4 | anbi2d 451 | . . . . 5 |
6 | findcard2d.ch | . . . . 5 | |
7 | 5, 6 | imbi12d 232 | . . . 4 |
8 | sseq1 3020 | . . . . . 6 | |
9 | 8 | anbi2d 451 | . . . . 5 |
10 | findcard2d.th | . . . . 5 | |
11 | 9, 10 | imbi12d 232 | . . . 4 |
12 | sseq1 3020 | . . . . . 6 | |
13 | 12 | anbi2d 451 | . . . . 5 |
14 | findcard2d.ta | . . . . 5 | |
15 | 13, 14 | imbi12d 232 | . . . 4 |
16 | sseq1 3020 | . . . . . 6 | |
17 | 16 | anbi2d 451 | . . . . 5 |
18 | findcard2d.et | . . . . 5 | |
19 | 17, 18 | imbi12d 232 | . . . 4 |
20 | findcard2d.z | . . . . 5 | |
21 | 20 | adantr 270 | . . . 4 |
22 | simprl 497 | . . . . . . . 8 | |
23 | simprr 498 | . . . . . . . . 9 | |
24 | 23 | unssad 3149 | . . . . . . . 8 |
25 | 22, 24 | jca 300 | . . . . . . 7 |
26 | id 19 | . . . . . . . . . . 11 | |
27 | vsnid 3426 | . . . . . . . . . . . 12 | |
28 | elun2 3140 | . . . . . . . . . . . 12 | |
29 | 27, 28 | mp1i 10 | . . . . . . . . . . 11 |
30 | 26, 29 | sseldd 3000 | . . . . . . . . . 10 |
31 | 30 | ad2antll 474 | . . . . . . . . 9 |
32 | simplr 496 | . . . . . . . . 9 | |
33 | 31, 32 | eldifd 2983 | . . . . . . . 8 |
34 | findcard2d.i | . . . . . . . 8 | |
35 | 22, 24, 33, 34 | syl12anc 1167 | . . . . . . 7 |
36 | 25, 35 | embantd 55 | . . . . . 6 |
37 | 36 | ex 113 | . . . . 5 |
38 | 37 | com23 77 | . . . 4 |
39 | 7, 11, 15, 19, 21, 38 | findcard2s 6374 | . . 3 |
40 | 3, 39 | mpcom 36 | . 2 |
41 | 1, 40 | mpan2 415 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wceq 1284 wcel 1433 cdif 2970 cun 2971 wss 2973 c0 3251 csn 3398 cfn 6244 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-coll 3893 ax-sep 3896 ax-nul 3904 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-setind 4280 ax-iinf 4329 |
This theorem depends on definitions: df-bi 115 df-dc 776 df-3or 920 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-rex 2354 df-reu 2355 df-rab 2357 df-v 2603 df-sbc 2816 df-csb 2909 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-if 3352 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-int 3637 df-iun 3680 df-br 3786 df-opab 3840 df-mpt 3841 df-tr 3876 df-id 4048 df-iord 4121 df-on 4123 df-suc 4126 df-iom 4332 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 df-fv 4930 df-er 6129 df-en 6245 df-fin 6247 |
This theorem is referenced by: (None) |
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