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Theorem feq2i 5236
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 5226 . 2 (𝐴 = 𝐵 → (𝐹:𝐴𝐶𝐹:𝐵𝐶))
31, 2ax-mp 5 1 (𝐹:𝐴𝐶𝐹:𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wb 104   = wceq 1316  wf 5089
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-4 1472  ax-17 1491  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-cleq 2110  df-fn 5096  df-f 5097
This theorem is referenced by:  fmpox  6066  fmpo  6067  tposf  6137  issmo  6153  tfrcllemsucfn  6218  1fv  9884  fxnn0nninf  10179  0met  12480  dvef  12783
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