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Mirrors > Home > ILE Home > Th. List > equs4 | Unicode version |
Description: Lemma used in proofs of substitution properties. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Mario Carneiro, 20-May-2014.) |
Ref | Expression |
---|---|
equs4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1586 | . . 3 | |
2 | 19.29 1511 | . . 3 | |
3 | 1, 2 | mpan2 401 | . 2 |
4 | ancl 301 | . . . 4 | |
5 | 4 | imp 115 | . . 3 |
6 | 5 | eximi 1491 | . 2 |
7 | 3, 6 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wceq 1243 wex 1381 |
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-4 1400 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: sb2 1650 equs45f 1683 |
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