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Theorem cbvsbc 3306
 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 2543 . . 3
54eleq2i 2480 . 2
6 df-sbc 3278 . 2
7 df-sbc 3278 . 2
85, 6, 73bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wnf 1637   wcel 1842  cab 2387  wsbc 3277 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-sbc 3278 This theorem is referenced by:  cbvsbcv  3307  cbvcsb  3378
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