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Mirrors > Home > ILE Home > Th. List > copsex2t | Unicode version |
Description: Closed theorem form of copsex2g 3983. (Contributed by NM, 17-Feb-2013.) |
Ref | Expression |
---|---|
copsex2t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2568 | . . . 4 | |
2 | elisset 2568 | . . . 4 | |
3 | 1, 2 | anim12i 321 | . . 3 |
4 | eeanv 1807 | . . 3 | |
5 | 3, 4 | sylibr 137 | . 2 |
6 | nfa1 1434 | . . . 4 | |
7 | nfe1 1385 | . . . . 5 | |
8 | nfv 1421 | . . . . 5 | |
9 | 7, 8 | nfbi 1481 | . . . 4 |
10 | nfa2 1471 | . . . . 5 | |
11 | nfe1 1385 | . . . . . . 7 | |
12 | 11 | nfex 1528 | . . . . . 6 |
13 | nfv 1421 | . . . . . 6 | |
14 | 12, 13 | nfbi 1481 | . . . . 5 |
15 | opeq12 3551 | . . . . . . . . 9 | |
16 | copsexg 3981 | . . . . . . . . . 10 | |
17 | 16 | eqcoms 2043 | . . . . . . . . 9 |
18 | 15, 17 | syl 14 | . . . . . . . 8 |
19 | 18 | adantl 262 | . . . . . . 7 |
20 | sp 1401 | . . . . . . . . 9 | |
21 | 20 | 19.21bi 1450 | . . . . . . . 8 |
22 | 21 | imp 115 | . . . . . . 7 |
23 | 19, 22 | bitr3d 179 | . . . . . 6 |
24 | 23 | ex 108 | . . . . 5 |
25 | 10, 14, 24 | exlimd 1488 | . . . 4 |
26 | 6, 9, 25 | exlimd 1488 | . . 3 |
27 | 26 | imp 115 | . 2 |
28 | 5, 27 | sylan2 270 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cop 3378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 |
This theorem is referenced by: opelopabt 3999 |
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