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Theorem sbceq1d 3167
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by NM, 30-Jun-2018.)
Hypothesis
Ref Expression
sbceq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
sbceq1d  |-  ( ph  ->  ( [. A  /  x ]. ps  <->  [. B  /  x ]. ps ) )

Proof of Theorem sbceq1d
StepHypRef Expression
1 sbceq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 dfsbcq 3164 . 2  |-  ( A  =  B  ->  ( [. A  /  x ]. ps  <->  [. B  /  x ]. ps ) )
31, 2syl 16 1  |-  ( ph  ->  ( [. A  /  x ]. ps  <->  [. B  /  x ]. ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    = wceq 1653   [.wsbc 3162
This theorem is referenced by:  sbceq1dd  3168
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 2418
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-cleq 2430  df-clel 2433  df-sbc 3163
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