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Mirrors > Home > ILE Home > Th. List > copsex2g | Unicode version |
Description: Implicit substitution inference for ordered pairs. (Contributed by NM, 28-May-1995.) |
Ref | Expression |
---|---|
copsex2g.1 |
Ref | Expression |
---|---|
copsex2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2568 | . 2 | |
2 | elisset 2568 | . 2 | |
3 | eeanv 1807 | . . 3 | |
4 | nfe1 1385 | . . . . 5 | |
5 | nfv 1421 | . . . . 5 | |
6 | 4, 5 | nfbi 1481 | . . . 4 |
7 | nfe1 1385 | . . . . . . 7 | |
8 | 7 | nfex 1528 | . . . . . 6 |
9 | nfv 1421 | . . . . . 6 | |
10 | 8, 9 | nfbi 1481 | . . . . 5 |
11 | opeq12 3551 | . . . . . . 7 | |
12 | copsexg 3981 | . . . . . . . 8 | |
13 | 12 | eqcoms 2043 | . . . . . . 7 |
14 | 11, 13 | syl 14 | . . . . . 6 |
15 | copsex2g.1 | . . . . . 6 | |
16 | 14, 15 | bitr3d 179 | . . . . 5 |
17 | 10, 16 | exlimi 1485 | . . . 4 |
18 | 6, 17 | exlimi 1485 | . . 3 |
19 | 3, 18 | sylbir 125 | . 2 |
20 | 1, 2, 19 | syl2an 273 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 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: opelopabga 4000 ov6g 5638 ltresr 6915 |
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