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Theorem fneq2i 4937
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 4931 . 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 98   = wceq 1242   Fn wfn 4840
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-fn 4848
This theorem is referenced by:  fnunsn  4949  tpos0  5830
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