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Theorem cbvsbc 3189
 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 2554 . . 3
54eleq2i 2500 . 2
6 df-sbc 3162 . 2
7 df-sbc 3162 . 2
85, 6, 73bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wnf 1553   wcel 1725  cab 2422  wsbc 3161 This theorem is referenced by:  cbvsbcv  3190  cbvcsb  3255 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-sbc 3162
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