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Mirrors > Home > ILE Home > Th. List > copsex2t | Unicode version |
Description: Closed theorem form of copsex2g 4168. (Contributed by NM, 17-Feb-2013.) |
Ref | Expression |
---|---|
copsex2t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2700 | . . . 4 | |
2 | elisset 2700 | . . . 4 | |
3 | 1, 2 | anim12i 336 | . . 3 |
4 | eeanv 1904 | . . 3 | |
5 | 3, 4 | sylibr 133 | . 2 |
6 | nfa1 1521 | . . . 4 | |
7 | nfe1 1472 | . . . . 5 | |
8 | nfv 1508 | . . . . 5 | |
9 | 7, 8 | nfbi 1568 | . . . 4 |
10 | nfa2 1558 | . . . . 5 | |
11 | nfe1 1472 | . . . . . . 7 | |
12 | 11 | nfex 1616 | . . . . . 6 |
13 | nfv 1508 | . . . . . 6 | |
14 | 12, 13 | nfbi 1568 | . . . . 5 |
15 | opeq12 3707 | . . . . . . . . 9 | |
16 | copsexg 4166 | . . . . . . . . . 10 | |
17 | 16 | eqcoms 2142 | . . . . . . . . 9 |
18 | 15, 17 | syl 14 | . . . . . . . 8 |
19 | 18 | adantl 275 | . . . . . . 7 |
20 | sp 1488 | . . . . . . . . 9 | |
21 | 20 | 19.21bi 1537 | . . . . . . . 8 |
22 | 21 | imp 123 | . . . . . . 7 |
23 | 19, 22 | bitr3d 189 | . . . . . 6 |
24 | 23 | ex 114 | . . . . 5 |
25 | 10, 14, 24 | exlimd 1576 | . . . 4 |
26 | 6, 9, 25 | exlimd 1576 | . . 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 1329 wceq 1331 wex 1468 wcel 1480 cop 3530 |
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 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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 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-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 |
This theorem is referenced by: opelopabt 4184 |
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