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Mirrors > Home > ILE Home > Th. List > copsex2t | Unicode version |
Description: Closed theorem form of copsex2g 4001. (Contributed by NM, 17-Feb-2013.) |
Ref | Expression |
---|---|
copsex2t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2613 | . . . 4 | |
2 | elisset 2613 | . . . 4 | |
3 | 1, 2 | anim12i 331 | . . 3 |
4 | eeanv 1848 | . . 3 | |
5 | 3, 4 | sylibr 132 | . 2 |
6 | nfa1 1474 | . . . 4 | |
7 | nfe1 1425 | . . . . 5 | |
8 | nfv 1461 | . . . . 5 | |
9 | 7, 8 | nfbi 1521 | . . . 4 |
10 | nfa2 1511 | . . . . 5 | |
11 | nfe1 1425 | . . . . . . 7 | |
12 | 11 | nfex 1568 | . . . . . 6 |
13 | nfv 1461 | . . . . . 6 | |
14 | 12, 13 | nfbi 1521 | . . . . 5 |
15 | opeq12 3572 | . . . . . . . . 9 | |
16 | copsexg 3999 | . . . . . . . . . 10 | |
17 | 16 | eqcoms 2084 | . . . . . . . . 9 |
18 | 15, 17 | syl 14 | . . . . . . . 8 |
19 | 18 | adantl 271 | . . . . . . 7 |
20 | sp 1441 | . . . . . . . . 9 | |
21 | 20 | 19.21bi 1490 | . . . . . . . 8 |
22 | 21 | imp 122 | . . . . . . 7 |
23 | 19, 22 | bitr3d 188 | . . . . . 6 |
24 | 23 | ex 113 | . . . . 5 |
25 | 10, 14, 24 | exlimd 1528 | . . . 4 |
26 | 6, 9, 25 | exlimd 1528 | . . 3 |
27 | 26 | imp 122 | . 2 |
28 | 5, 27 | sylan2 280 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 cop 3401 |
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-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-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 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-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 |
This theorem is referenced by: opelopabt 4017 |
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