Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2735 | . 2 | |
2 | elisset 2735 | . 2 | |
3 | eeanv 1919 | . . 3 | |
4 | nfe1 1483 | . . . . 5 | |
5 | nfv 1515 | . . . . 5 | |
6 | 4, 5 | nfbi 1576 | . . . 4 |
7 | nfe1 1483 | . . . . . . 7 | |
8 | 7 | nfex 1624 | . . . . . 6 |
9 | nfv 1515 | . . . . . 6 | |
10 | 8, 9 | nfbi 1576 | . . . . 5 |
11 | opeq12 3754 | . . . . . . 7 | |
12 | copsexg 4216 | . . . . . . . 8 | |
13 | 12 | eqcoms 2167 | . . . . . . 7 |
14 | 11, 13 | syl 14 | . . . . . 6 |
15 | copsex2g.1 | . . . . . 6 | |
16 | 14, 15 | bitr3d 189 | . . . . 5 |
17 | 10, 16 | exlimi 1581 | . . . 4 |
18 | 6, 17 | exlimi 1581 | . . 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 1342 wex 1479 wcel 2135 cop 3573 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 |
This theorem is referenced by: opelopabga 4235 ov6g 5970 ltresr 7771 |
Copyright terms: Public domain | W3C validator |