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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 1939 | . . . 4 |
3 | cbvab.1 | . . . . . 6 | |
4 | cbvab.3 | . . . . . . . 8 | |
5 | 4 | equcoms 1701 | . . . . . . 7 |
6 | 5 | bicomd 140 | . . . . . 6 |
7 | 3, 6 | sbie 1784 | . . . . 5 |
8 | sbequ 1833 | . . . . 5 | |
9 | 7, 8 | bitr3id 193 | . . . 4 |
10 | 2, 9 | sbie 1784 | . . 3 |
11 | df-clab 2157 | . . 3 | |
12 | df-clab 2157 | . . 3 | |
13 | 10, 11, 12 | 3bitr4i 211 | . 2 |
14 | 13 | eqriv 2167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 wnf 1453 wsb 1755 wcel 2141 cab 2156 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 |
This theorem is referenced by: cbvabv 2295 cbvrab 2728 cbvsbc 2983 cbvrabcsf 3114 dfdmf 4802 dfrnf 4850 funfvdm2f 5559 abrexex2g 6096 abrexex2 6100 |
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