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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 2160 | . . 3 |
5 | 4 | eleq2i 2104 | . 2 |
6 | df-sbc 2765 | . 2 | |
7 | df-sbc 2765 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wnf 1349 wcel 1393 cab 2026 wsbc 2764 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-sbc 2765 |
This theorem is referenced by: cbvsbcv 2792 cbvcsb 2856 |
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