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Theorem fneq2i 5306
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 5300 . 2  |-  ( A  =  B  ->  ( F  Fn  A  <->  F  Fn  B ) )
31, 2ax-mp 5 1  |-  ( F  Fn  A  <->  F  Fn  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 105    = wceq 1353    Fn wfn 5206
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-fn 5214
This theorem is referenced by:  fnunsn  5318  tpos0  6268  dfixp  6693  ser0f  10488
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