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Mirrors > Home > ILE Home > Th. List > equvin | Unicode version |
Description: A variable introduction law for equality. Lemma 15 of [Monk2] p. 109. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
equvin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equvini 1732 | . 2 | |
2 | ax-17 1507 | . . 3 | |
3 | equtr 1686 | . . . 4 | |
4 | 3 | imp 123 | . . 3 |
5 | 2, 4 | exlimih 1573 | . 2 |
6 | 1, 5 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wex 1469 |
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 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-i12 1486 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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