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Theorem feq23i 5952
 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 5942 . 2 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
41, 2, 3mp2an 704 1 (𝐹:𝐴𝐵𝐹:𝐶𝐷)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   = wceq 1475  ⟶wf 5800 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-in 3547  df-ss 3554  df-fn 5807  df-f 5808 This theorem is referenced by:  ftpg  6328  hashf  12987  funcoppc  16358  cnextfval  21676  uhgr0  25739  lfgredgge2  25790  uhgra0v  25839  wlkntrllem1  26089  mbfmvolf  29655  eulerpartlemt  29760  ismgmOLD  32819  elghomOLD  32856  tendoset  35065  pwssplit4  36677  lincdifsn  42007
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