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Theorem fneq2i 5323
Description: Equality inference for function predicate with domain. (Contributed by NM, 4-Sep-2011.)
Hypothesis
Ref Expression
fneq2i.1 𝐴 = 𝐵
Assertion
Ref Expression
fneq2i (𝐹 Fn 𝐴𝐹 Fn 𝐵)

Proof of Theorem fneq2i
StepHypRef Expression
1 fneq2i.1 . 2 𝐴 = 𝐵
2 fneq2 5317 . 2 (𝐴 = 𝐵 → (𝐹 Fn 𝐴𝐹 Fn 𝐵))
31, 2ax-mp 5 1 (𝐹 Fn 𝐴𝐹 Fn 𝐵)
Colors of variables: wff set class
Syntax hints:  wb 105   = wceq 1363   Fn wfn 5223
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-4 1520  ax-17 1536  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-cleq 2180  df-fn 5231
This theorem is referenced by:  fnunsn  5335  tpos0  6289  dfixp  6714  ser0f  10529  fnpr2o  12777
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