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Theorem cbvcsbv 3086
Description: Change the bound variable of a proper substitution into a class using implicit substitution. (Contributed by NM, 30-Sep-2008.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypothesis
Ref Expression
cbvcsbv.1  |-  ( x  =  y  ->  B  =  C )
Assertion
Ref Expression
cbvcsbv  |-  [_ A  /  x ]_ B  = 
[_ A  /  y ]_ C
Distinct variable groups:    x, y    y, B    x, C
Allowed substitution hints:    A( x, y)    B( x)    C( y)

Proof of Theorem cbvcsbv
StepHypRef Expression
1 nfcv 2419 . 2  |-  F/_ y B
2 nfcv 2419 . 2  |-  F/_ x C
3 cbvcsbv.1 . 2  |-  ( x  =  y  ->  B  =  C )
41, 2, 3cbvcsb 3085 1  |-  [_ A  /  x ]_ B  = 
[_ A  /  y ]_ C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   [_csb 3081
This theorem is referenced by:  cdleme40v  30658
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-sbc 2992  df-csb 3082
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