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Theorem fneq2d 5176
Description: Equality deduction for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
fneq2d.1 (φA = B)
Assertion
Ref Expression
fneq2d (φ → (F Fn AF Fn B))

Proof of Theorem fneq2d
StepHypRef Expression
1 fneq2d.1 . 2 (φA = B)
2 fneq2 5174 . 2 (A = B → (F Fn AF Fn B))
31, 2syl 15 1 (φ → (F Fn AF Fn B))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   = wceq 1642   Fn wfn 4776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-fn 4790
This theorem is referenced by:  fneq12d  5177
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