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Theorem sbceq2a 3304
Description: Equality theorem for class substitution. Class version of sbequ12r 1949. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a  |-  ( A  =  x  ->  ( [. A  /  x ]. ph  <->  ph ) )

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 3303 . . 3  |-  ( x  =  A  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
21eqcoms 2466 . 2  |-  ( A  =  x  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
32bicomd 201 1  |-  ( A  =  x  ->  ( [. A  /  x ]. ph  <->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    = wceq 1370   [.wsbc 3292
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-sbc 3293
This theorem is referenced by:  tfindes  6582  indexa  28774  fdc  28788  fdc1  28789  alrimii  29074  rabssnn0fi  30894  tratrbVD  31914
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