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Theorem fneq2i 5062
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 5056 . 2 (𝐴 = 𝐵 → (𝐹 Fn 𝐴𝐹 Fn 𝐵))
31, 2ax-mp 7 1 (𝐹 Fn 𝐴𝐹 Fn 𝐵)
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1285   Fn wfn 4964
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 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-fn 4972
This theorem is referenced by:  fnunsn  5074  tpos0  5971  iser0f  9788
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