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Theorem cbvsbc 2791
 Description: Change bound variables in a wff substitution. (Contributed by Jeff Hankins, 19-Sep-2009.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypotheses
Ref Expression
cbvsbc.1
cbvsbc.2
cbvsbc.3
Assertion
Ref Expression
cbvsbc

Proof of Theorem cbvsbc
StepHypRef Expression
1 cbvsbc.1 . . . 4
2 cbvsbc.2 . . . 4
3 cbvsbc.3 . . . 4
41, 2, 3cbvab 2160 . . 3
54eleq2i 2104 . 2
6 df-sbc 2765 . 2
7 df-sbc 2765 . 2
85, 6, 73bitr4i 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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