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Mirrors > Home > ILE Home > Th. List > equsalh | Unicode version |
Description: A useful equivalence related to substitution. New proofs should use equsal 1615 instead. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
equsalh.1 | |
equsalh.2 |
Ref | Expression |
---|---|
equsalh |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsalh.2 | . . . . 5 | |
2 | equsalh.1 | . . . . . 6 | |
3 | 2 | 19.3h 1445 | . . . . 5 |
4 | 1, 3 | syl6bbr 187 | . . . 4 |
5 | 4 | pm5.74i 169 | . . 3 |
6 | 5 | albii 1359 | . 2 |
7 | 2 | a1d 22 | . . . 4 |
8 | 2, 7 | alrimih 1358 | . . 3 |
9 | ax9o 1588 | . . 3 | |
10 | 8, 9 | impbii 117 | . 2 |
11 | 6, 10 | bitr4i 176 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 |
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: sb6x 1662 dvelimfALT2 1698 dvelimALT 1886 dvelimfv 1887 dvelimor 1894 |
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