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Mirrors > Home > ILE Home > Th. List > cbvalv1 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. Version of cbval 1734 with a disjoint variable condition. See cbvalvw 1899 for a version with two disjoint variable conditions, and cbvalv 1897 for another variant. (Contributed by NM, 13-May-1993.) (Revised by BJ, 31-May-2019.) |
Ref | Expression |
---|---|
cbvalv1.nf1 | |
cbvalv1.nf2 | |
cbvalv1.1 |
Ref | Expression |
---|---|
cbvalv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvalv1.nf1 | . . 3 | |
2 | cbvalv1.nf2 | . . 3 | |
3 | cbvalv1.1 | . . . 4 | |
4 | 3 | biimpd 143 | . . 3 |
5 | 1, 2, 4 | cbv3v 1724 | . 2 |
6 | 3 | biimprd 157 | . . . 4 |
7 | 6 | equcoms 1688 | . . 3 |
8 | 2, 1, 7 | cbv3v 1724 | . 2 |
9 | 5, 8 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1333 wnf 1440 |
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-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1441 |
This theorem is referenced by: (None) |
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