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Theorem feq23i 6663
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:𝐴𝐵𝐹:𝐶𝐷)

Proof of Theorem feq23i
StepHypRef Expression
1 feq23i.1 . 2 𝐴 = 𝐶
2 feq23i.2 . 2 𝐵 = 𝐷
3 feq23 6653 . 2 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
41, 2, 3mp2an 691 1 (𝐹:𝐴𝐵𝐹:𝐶𝐷)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1542  wf 6493
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-in 3918  df-ss 3928  df-fn 6500  df-f 6501
This theorem is referenced by:  ftpg  7103  hashf  14244  funcoppc  17766  cnextfval  23429  uhgr0  28066  lfgredgge2  28117  mbfmvolf  32923  eulerpartlemt  33028  ismgmOLD  36355  elghomOLD  36392  tendoset  39268  pwssplit4  41459  isomushgr  46104  lincdifsn  46591
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