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Mirrors > Home > ILE Home > Th. List > cbv1 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. Revised to format hypotheses to common style. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Revised by Wolf Lammen, 13-May-2018.) |
Ref | Expression |
---|---|
cbv1.1 | |
cbv1.2 | |
cbv1.3 | |
cbv1.4 | |
cbv1.5 |
Ref | Expression |
---|---|
cbv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbv1.2 | . . . . 5 | |
2 | cbv1.3 | . . . . 5 | |
3 | 1, 2 | nfim1 1463 | . . . 4 |
4 | cbv1.1 | . . . . 5 | |
5 | cbv1.4 | . . . . 5 | |
6 | 4, 5 | nfim1 1463 | . . . 4 |
7 | cbv1.5 | . . . . . 6 | |
8 | 7 | com12 27 | . . . . 5 |
9 | 8 | a2d 23 | . . . 4 |
10 | 3, 6, 9 | cbv3 1630 | . . 3 |
11 | 4 | 19.21 1475 | . . 3 |
12 | 1 | 19.21 1475 | . . 3 |
13 | 10, 11, 12 | 3imtr3i 189 | . 2 |
14 | 13 | pm2.86i 92 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wnf 1349 |
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-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: cbv1h 1633 |
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