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Theorem feq2d 5066
Description: Equality deduction for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
feq2d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
feq2d  |-  ( ph  ->  ( F : A --> C 
<->  F : B --> C ) )

Proof of Theorem feq2d
StepHypRef Expression
1 feq2d.1 . 2  |-  ( ph  ->  A  =  B )
2 feq2 5062 . 2  |-  ( A  =  B  ->  ( F : A --> C  <->  F : B
--> C ) )
31, 2syl 14 1  |-  ( ph  ->  ( F : A --> C 
<->  F : B --> C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    = wceq 1285   -->wf 4928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-fn 4935  df-f 4936
This theorem is referenced by:  feq12d  5067  ffdm  5092  fsng  5368  issmo2  5938  qliftf  6257  fseq1p1m1  9187  fseq1m1p1  9188  iseqfclt  9536
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