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Theorem feq23i 5546
Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypotheses
Ref Expression
feq23i.1  |-  A  =  C
feq23i.2  |-  B  =  D
Assertion
Ref Expression
feq23i  |-  ( F : A --> B  <->  F : C
--> D )

Proof of Theorem feq23i
StepHypRef Expression
1 feq23i.1 . 2  |-  A  =  C
2 feq23i.2 . 2  |-  B  =  D
3 feq23 5538 . 2  |-  ( ( A  =  C  /\  B  =  D )  ->  ( F : A --> B 
<->  F : C --> D ) )
41, 2, 3mp2an 654 1  |-  ( F : A --> B  <->  F : C
--> D )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1649   -->wf 5409
This theorem is referenced by:  ftpg  5875  funcoppc  14027  cnextfval  18046  uhgra0v  21298  wlkntrllem1  21512  ismgm  21861  elghom  21904  mbfmvolf  24569  pwssplit4  27059  tendoset  31241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-in 3287  df-ss 3294  df-fn 5416  df-f 5417
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