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Mirrors > Home > ILE Home > Th. List > eqvincg | Unicode version |
Description: A variable introduction law for class equality, deduction version. (Contributed by Thierry Arnoux, 2-Mar-2017.) |
Ref | Expression |
---|---|
eqvincg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2735 | . . . 4 | |
2 | ax-1 6 | . . . . . 6 | |
3 | eqtr 2182 | . . . . . . 7 | |
4 | 3 | ex 114 | . . . . . 6 |
5 | 2, 4 | jca 304 | . . . . 5 |
6 | 5 | eximi 1587 | . . . 4 |
7 | pm3.43 592 | . . . . 5 | |
8 | 7 | eximi 1587 | . . . 4 |
9 | 1, 6, 8 | 3syl 17 | . . 3 |
10 | nfv 1515 | . . . 4 | |
11 | 10 | 19.37-1 1661 | . . 3 |
12 | 9, 11 | syl 14 | . 2 |
13 | eqtr2 2183 | . . 3 | |
14 | 13 | exlimiv 1585 | . 2 |
15 | 12, 14 | impbid1 141 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wex 1479 wcel 2135 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-v 2723 |
This theorem is referenced by: dff13 5730 f1eqcocnv 5753 |
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