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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 2738 | . . . 4 |
3 | ax-1 6 | . . . . . 6 | |
4 | eqtr 2188 | . . . . . . 7 | |
5 | 4 | ex 114 | . . . . . 6 |
6 | 3, 5 | jca 304 | . . . . 5 |
7 | 6 | eximi 1593 | . . . 4 |
8 | pm3.43 597 | . . . . 5 | |
9 | 8 | eximi 1593 | . . . 4 |
10 | 2, 7, 9 | mp2b 8 | . . 3 |
11 | 10 | 19.37aiv 1668 | . 2 |
12 | eqtr2 2189 | . . 3 | |
13 | 12 | exlimiv 1591 | . 2 |
14 | 11, 13 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wex 1485 wcel 2141 cvv 2730 |
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-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: eqvincf 2855 |
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