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Mirrors > Home > ILE Home > Th. List > eqvinc | Unicode version |
Description: A variable introduction law for class equality. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
eqvinc.1 |
Ref | Expression |
---|---|
eqvinc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqvinc.1 | . . . . 5 | |
2 | 1 | isseti 2607 | . . . 4 |
3 | ax-1 5 | . . . . . 6 | |
4 | eqtr 2098 | . . . . . . 7 | |
5 | 4 | ex 113 | . . . . . 6 |
6 | 3, 5 | jca 300 | . . . . 5 |
7 | 6 | eximi 1531 | . . . 4 |
8 | pm3.43 566 | . . . . 5 | |
9 | 8 | eximi 1531 | . . . 4 |
10 | 2, 7, 9 | mp2b 8 | . . 3 |
11 | 10 | 19.37aiv 1605 | . 2 |
12 | eqtr2 2099 | . . 3 | |
13 | 12 | exlimiv 1529 | . 2 |
14 | 11, 13 | impbii 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wex 1421 wcel 1433 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: eqvincf 2720 |
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