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Theorem fneq2i 5062
Description: Equality inference for function predicate with domain. (Contributed by NM, 4-Sep-2011.)
Hypothesis
Ref Expression
fneq2i.1  |-  A  =  B
Assertion
Ref Expression
fneq2i  |-  ( F  Fn  A  <->  F  Fn  B )

Proof of Theorem fneq2i
StepHypRef Expression
1 fneq2i.1 . 2  |-  A  =  B
2 fneq2 5056 . 2  |-  ( A  =  B  ->  ( F  Fn  A  <->  F  Fn  B ) )
31, 2ax-mp 7 1  |-  ( F  Fn  A  <->  F  Fn  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1285    Fn wfn 4964
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 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-fn 4972
This theorem is referenced by:  fnunsn  5074  tpos0  5971  iser0f  9788
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