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Theorem fneq2d 5214
Description: Equality deduction for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
fneq2d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
fneq2d  |-  ( ph  ->  ( F  Fn  A  <->  F  Fn  B ) )

Proof of Theorem fneq2d
StepHypRef Expression
1 fneq2d.1 . 2  |-  ( ph  ->  A  =  B )
2 fneq2 5212 . 2  |-  ( A  =  B  ->  ( F  Fn  A  <->  F  Fn  B ) )
31, 2syl 14 1  |-  ( ph  ->  ( F  Fn  A  <->  F  Fn  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    = wceq 1331    Fn wfn 5118
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-4 1487  ax-17 1506  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-fn 5126
This theorem is referenced by:  fneq12d  5215  acfun  7063  ccfunen  7079  seq3shft  10617
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