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Theorem feq2d 5063
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 5059 . 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 102   = wceq 1259  wf 4926
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-fn 4933  df-f 4934
This theorem is referenced by:  feq12d  5064  ffdm  5089  fsng  5364  issmo2  5935  qliftf  6222  fseq1p1m1  9058  fseq1m1p1  9059
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