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Theorem feq23i 5528
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 5520 . 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 5391
This theorem is referenced by:  ftpg  5856  funcoppc  14000  cnextfval  18015  uhgra0v  21213  wlkntrllem1  21414  wlkntrllem3  21416  ismgm  21757  elghom  21800  mbfmvolf  24411  pwssplit4  26861  tendoset  30874
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 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
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 2375  df-cleq 2381  df-clel 2384  df-in 3271  df-ss 3278  df-fn 5398  df-f 5399
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