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Mirrors > Home > ILE Home > Th. List > copsex2t | Unicode version |
Description: Closed theorem form of copsex2g 4138. (Contributed by NM, 17-Feb-2013.) |
Ref | Expression |
---|---|
copsex2t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2674 | . . . 4 | |
2 | elisset 2674 | . . . 4 | |
3 | 1, 2 | anim12i 336 | . . 3 |
4 | eeanv 1884 | . . 3 | |
5 | 3, 4 | sylibr 133 | . 2 |
6 | nfa1 1506 | . . . 4 | |
7 | nfe1 1457 | . . . . 5 | |
8 | nfv 1493 | . . . . 5 | |
9 | 7, 8 | nfbi 1553 | . . . 4 |
10 | nfa2 1543 | . . . . 5 | |
11 | nfe1 1457 | . . . . . . 7 | |
12 | 11 | nfex 1601 | . . . . . 6 |
13 | nfv 1493 | . . . . . 6 | |
14 | 12, 13 | nfbi 1553 | . . . . 5 |
15 | opeq12 3677 | . . . . . . . . 9 | |
16 | copsexg 4136 | . . . . . . . . . 10 | |
17 | 16 | eqcoms 2120 | . . . . . . . . 9 |
18 | 15, 17 | syl 14 | . . . . . . . 8 |
19 | 18 | adantl 275 | . . . . . . 7 |
20 | sp 1473 | . . . . . . . . 9 | |
21 | 20 | 19.21bi 1522 | . . . . . . . 8 |
22 | 21 | imp 123 | . . . . . . 7 |
23 | 19, 22 | bitr3d 189 | . . . . . 6 |
24 | 23 | ex 114 | . . . . 5 |
25 | 10, 14, 24 | exlimd 1561 | . . . 4 |
26 | 6, 9, 25 | exlimd 1561 | . . 3 |
27 | 26 | imp 123 | . 2 |
28 | 5, 27 | sylan2 284 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wex 1453 wcel 1465 cop 3500 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 |
This theorem is referenced by: opelopabt 4154 |
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