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Theorem feq23i 6276
 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 6266 . 2 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
41, 2, 3mp2an 683 1 (𝐹:𝐴𝐵𝐹:𝐶𝐷)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 198   = wceq 1656  ⟶wf 6123 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-in 3805  df-ss 3812  df-fn 6130  df-f 6131 This theorem is referenced by:  ftpg  6679  hashf  13425  funcoppc  16894  cnextfval  22243  uhgr0  26378  lfgredgge2  26429  mbfmvolf  30869  eulerpartlemt  30974  ismgmOLD  34186  elghomOLD  34223  tendoset  36829  pwssplit4  38497  isomushgr  42558  lincdifsn  43074
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