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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 2563 | . . . 4 |
3 | ax-1 5 | . . . . . 6 | |
4 | eqtr 2057 | . . . . . . 7 | |
5 | 4 | ex 108 | . . . . . 6 |
6 | 3, 5 | jca 290 | . . . . 5 |
7 | 6 | eximi 1491 | . . . 4 |
8 | pm3.43 534 | . . . . 5 | |
9 | 8 | eximi 1491 | . . . 4 |
10 | 2, 7, 9 | mp2b 8 | . . 3 |
11 | 10 | 19.37aiv 1565 | . 2 |
12 | eqtr2 2058 | . . 3 | |
13 | 12 | exlimiv 1489 | . 2 |
14 | 11, 13 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 cvv 2557 |
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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: eqvincf 2669 |
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