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Mirrors > Home > ILE Home > Th. List > cbv2 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. Revised to align format of 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 |
---|---|
cbv2.1 | |
cbv2.2 | |
cbv2.3 | |
cbv2.4 | |
cbv2.5 |
Ref | Expression |
---|---|
cbv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbv2.2 | . . . 4 | |
2 | 1 | nfri 1412 | . . 3 |
3 | cbv2.1 | . . . . 5 | |
4 | 3 | nfal 1468 | . . . 4 |
5 | 4 | nfri 1412 | . . 3 |
6 | 2, 5 | syl 14 | . 2 |
7 | cbv2.3 | . . . 4 | |
8 | 7 | nfrd 1413 | . . 3 |
9 | cbv2.4 | . . . 4 | |
10 | 9 | nfrd 1413 | . . 3 |
11 | cbv2.5 | . . 3 | |
12 | 8, 10, 11 | cbv2h 1634 | . 2 |
13 | 6, 12 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 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-8 1395 ax-4 1400 ax-17 1419 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: cbvald 1800 cbvrald 9927 |
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