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Theorem feq23i 5558
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 5550 . 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 1369   -->wf 5419
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-in 3340  df-ss 3347  df-fn 5426  df-f 5427
This theorem is referenced by:  ftpg  5897  funcoppc  14790  cnextfval  19639  uhgra0v  23249  wlkntrllem1  23463  ismgm  23812  elghom  23855  mbfmvolf  26686  eulerpartlemt  26759  pwssplit4  29447  lincdifsn  30963  tendoset  34408
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