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Theorem sbceq1d 3009
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
sbceq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
sbceq1d  |-  ( ph  ->  ( [. A  /  x ]. ph  <->  [. B  /  x ]. ph ) )

Proof of Theorem sbceq1d
StepHypRef Expression
1 sbceq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 dfsbcq 3006 . 2  |-  ( A  =  B  ->  ( [. A  /  x ]. ph  <->  [. B  /  x ]. ph ) )
31, 2syl 15 1  |-  ( ph  ->  ( [. A  /  x ]. ph  <->  [. B  /  x ]. ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1632   [.wsbc 3004
This theorem is referenced by:  sbceq1dd  3010
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-cleq 2289  df-clel 2292  df-sbc 3005
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