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Mirrors > Home > ILE Home > Th. List > cbvsbc | Unicode version |
Description: Change bound variables in a wff substitution. (Contributed by Jeff Hankins, 19-Sep-2009.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
cbvsbc.1 | |
cbvsbc.2 | |
cbvsbc.3 |
Ref | Expression |
---|---|
cbvsbc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvsbc.1 | . . . 4 | |
2 | cbvsbc.2 | . . . 4 | |
3 | cbvsbc.3 | . . . 4 | |
4 | 1, 2, 3 | cbvab 2263 | . . 3 |
5 | 4 | eleq2i 2206 | . 2 |
6 | df-sbc 2910 | . 2 | |
7 | df-sbc 2910 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wnf 1436 wcel 1480 cab 2125 wsbc 2909 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-sbc 2910 |
This theorem is referenced by: cbvsbcv 2938 cbvcsb 3008 |
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