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Mirrors > Home > ILE Home > Th. List > cbvab | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
cbvab.1 | |
cbvab.2 | |
cbvab.3 |
Ref | Expression |
---|---|
cbvab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvab.2 | . . . . 5 | |
2 | 1 | nfsb 1863 | . . . 4 |
3 | cbvab.1 | . . . . . 6 | |
4 | cbvab.3 | . . . . . . . 8 | |
5 | 4 | equcoms 1634 | . . . . . . 7 |
6 | 5 | bicomd 139 | . . . . . 6 |
7 | 3, 6 | sbie 1714 | . . . . 5 |
8 | sbequ 1761 | . . . . 5 | |
9 | 7, 8 | syl5bbr 192 | . . . 4 |
10 | 2, 9 | sbie 1714 | . . 3 |
11 | df-clab 2068 | . . 3 | |
12 | df-clab 2068 | . . 3 | |
13 | 10, 11, 12 | 3bitr4i 210 | . 2 |
14 | 13 | eqriv 2078 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 wnf 1389 wcel 1433 wsb 1685 cab 2067 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 |
This theorem is referenced by: cbvabv 2202 cbvrab 2599 cbvsbc 2842 cbvrabcsf 2967 dfdmf 4546 dfrnf 4593 funfvdm2f 5259 abrexex2g 5767 abrexex2 5771 |
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