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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 2695 | . 2 | |
2 | elisset 2695 | . 2 | |
3 | eeanv 1902 | . . 3 | |
4 | nfe1 1472 | . . . . 5 | |
5 | nfv 1508 | . . . . 5 | |
6 | 4, 5 | nfbi 1568 | . . . 4 |
7 | nfe1 1472 | . . . . . . 7 | |
8 | 7 | nfex 1616 | . . . . . 6 |
9 | nfv 1508 | . . . . . 6 | |
10 | 8, 9 | nfbi 1568 | . . . . 5 |
11 | opeq12 3702 | . . . . . . 7 | |
12 | copsexg 4161 | . . . . . . . 8 | |
13 | 12 | eqcoms 2140 | . . . . . . 7 |
14 | 11, 13 | syl 14 | . . . . . 6 |
15 | copsex2g.1 | . . . . . 6 | |
16 | 14, 15 | bitr3d 189 | . . . . 5 |
17 | 10, 16 | exlimi 1573 | . . . 4 |
18 | 6, 17 | exlimi 1573 | . . 3 |
19 | 3, 18 | sylbir 134 | . 2 |
20 | 1, 2, 19 | syl2an 287 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 cop 3525 |
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 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 |
This theorem is referenced by: opelopabga 4180 ov6g 5901 ltresr 7640 |
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