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Theorem feq2i 5341
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 5331 . 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 1348  wf 5194
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 1440  ax-gen 1442  ax-4 1503  ax-17 1519  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-cleq 2163  df-fn 5201  df-f 5202
This theorem is referenced by:  fmpox  6179  fmpo  6180  tposf  6251  issmo  6267  tfrcllemsucfn  6332  1fv  10095  fxnn0nninf  10394  0met  13178  dvef  13482
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