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Theorem feq23i 5723
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 5714 . 2  |-  ( ( A  =  C  /\  B  =  D )  ->  ( F : A --> B 
<->  F : C --> D ) )
41, 2, 3mp2an 672 1  |-  ( F : A --> B  <->  F : C
--> D )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    = wceq 1379   -->wf 5582
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-in 3483  df-ss 3490  df-fn 5589  df-f 5590
This theorem is referenced by:  ftpg  6069  funcoppc  15098  cnextfval  20297  uhgra0v  23986  wlkntrllem1  24237  ismgm  24998  elghom  25041  mbfmvolf  27877  eulerpartlemt  27950  pwssplit4  30639  lincdifsn  32098  tendoset  35555
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