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Theorem feq23i 6077
 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 6067 . 2 ((𝐴 = 𝐶𝐵 = 𝐷) → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
41, 2, 3mp2an 708 1 (𝐹:𝐴𝐵𝐹:𝐶𝐷)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196   = wceq 1523  ⟶wf 5922 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-in 3614  df-ss 3621  df-fn 5929  df-f 5930 This theorem is referenced by:  ftpg  6463  hashf  13165  funcoppc  16582  cnextfval  21913  uhgr0  26013  lfgredgge2  26064  mbfmvolf  30456  eulerpartlemt  30561  ismgmOLD  33779  elghomOLD  33816  tendoset  36364  pwssplit4  37976  lincdifsn  42538
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