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Theorem sbceq2a 3174
Description: Equality theorem for class substitution. Class version of sbequ12r 1946. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a  |-  ( A  =  x  ->  ( [. A  /  x ]. ph  <->  ph ) )

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 3173 . . 3  |-  ( x  =  A  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
21eqcoms 2441 . 2  |-  ( A  =  x  ->  ( ph 
<-> 
[. A  /  x ]. ph ) )
32bicomd 194 1  |-  ( A  =  x  ->  ( [. A  /  x ]. ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    = wceq 1653   [.wsbc 3163
This theorem is referenced by:  tfindes  4844  indexa  26437  fdc  26451  fdc1  26452  tratrbVD  29035
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-sbc 3164
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