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Mirrors > Home > ILE Home > Th. List > cbvalh | Unicode version |
Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
cbvalh.1 | |
cbvalh.2 | |
cbvalh.3 |
Ref | Expression |
---|---|
cbvalh |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvalh.1 | . . 3 | |
2 | cbvalh.2 | . . 3 | |
3 | cbvalh.3 | . . . 4 | |
4 | 3 | biimpd 142 | . . 3 |
5 | 1, 2, 4 | cbv3h 1671 | . 2 |
6 | 3 | equcoms 1634 | . . . 4 |
7 | 6 | biimprd 156 | . . 3 |
8 | 2, 1, 7 | cbv3h 1671 | . 2 |
9 | 5, 8 | impbii 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-nf 1390 |
This theorem is referenced by: cbval 1677 sb8h 1775 cbvalv 1835 sb9v 1895 sb8euh 1964 |
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