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Mirrors > Home > ILE Home > Th. List > eqvincf | Unicode version |
Description: A variable introduction law for class equality, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 14-Sep-2003.) |
Ref | Expression |
---|---|
eqvincf.1 | |
eqvincf.2 | |
eqvincf.3 |
Ref | Expression |
---|---|
eqvincf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqvincf.3 | . . 3 | |
2 | 1 | eqvinc 2844 | . 2 |
3 | eqvincf.1 | . . . . 5 | |
4 | 3 | nfeq2 2318 | . . . 4 |
5 | eqvincf.2 | . . . . 5 | |
6 | 5 | nfeq2 2318 | . . . 4 |
7 | 4, 6 | nfan 1552 | . . 3 |
8 | nfv 1515 | . . 3 | |
9 | eqeq1 2171 | . . . 4 | |
10 | eqeq1 2171 | . . . 4 | |
11 | 9, 10 | anbi12d 465 | . . 3 |
12 | 7, 8, 11 | cbvex 1743 | . 2 |
13 | 2, 12 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1342 wex 1479 wcel 2135 wnfc 2293 cvv 2721 |
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-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 |
This theorem is referenced by: (None) |
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