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Theorem feq2d 5115
Description: Equality deduction for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
feq2d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
feq2d (𝜑 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))

Proof of Theorem feq2d
StepHypRef Expression
1 feq2d.1 . 2 (𝜑𝐴 = 𝐵)
2 feq2 5111 . 2 (𝐴 = 𝐵 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))
31, 2syl 14 1 (𝜑 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103   = wceq 1287  wf 4977
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-4 1443  ax-17 1462  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-cleq 2078  df-fn 4984  df-f 4985
This theorem is referenced by:  feq12d  5116  ffdm  5145  fsng  5433  issmo2  6008  qliftf  6329  elpm2r  6375  casef  6723  fseq1p1m1  9438  fseq1m1p1  9439  iseqfclt  9794
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