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Theorem sbceq1dd 3010
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypotheses
Ref Expression
sbceq1d.1  |-  ( ph  ->  A  =  B )
sbceq1dd.2  |-  ( ph  ->  [. A  /  x ]. ph )
Assertion
Ref Expression
sbceq1dd  |-  ( ph  ->  [. B  /  x ]. ph )

Proof of Theorem sbceq1dd
StepHypRef Expression
1 sbceq1dd.2 . 2  |-  ( ph  ->  [. A  /  x ]. ph )
2 sbceq1d.1 . . 3  |-  ( ph  ->  A  =  B )
32sbceq1d 3009 . 2  |-  ( ph  ->  ( [. A  /  x ]. ph  <->  [. B  /  x ]. ph ) )
41, 3mpbid 201 1  |-  ( ph  ->  [. B  /  x ]. ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632   [.wsbc 3004
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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