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Theorem feq2i 5155
Description: Equality inference for functions. (Contributed by NM, 5-Sep-2011.)
Hypothesis
Ref Expression
feq2i.1 𝐴 = 𝐵
Assertion
Ref Expression
feq2i (𝐹:𝐴𝐶𝐹:𝐵𝐶)

Proof of Theorem feq2i
StepHypRef Expression
1 feq2i.1 . 2 𝐴 = 𝐵
2 feq2 5146 . 2 (𝐴 = 𝐵 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))
31, 2ax-mp 7 1 (𝐹:𝐴𝐶𝐹:𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1289  wf 5011
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 1381  ax-gen 1383  ax-4 1445  ax-17 1464  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-fn 5018  df-f 5019
This theorem is referenced by:  fmpt2x  5970  fmpt2  5971  tposf  6037  issmo  6053  tfrcllemsucfn  6118  1fv  9550  fxnn0nninf  9844  iseqfcl  9878
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