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Theorem cbvsbc 3356
 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 2598 . . 3
54eleq2i 2535 . 2
6 df-sbc 3328 . 2
7 df-sbc 3328 . 2
85, 6, 73bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  F/wnf 1616  e.wcel 1818  {cab 2442  [.wsbc 3327 This theorem is referenced by:  cbvsbcv  3357  cbvcsb  3439 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-sbc 3328
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