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Theorem fnfund 6604
Description: A function with domain is a function, deduction form. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
fnfund.1 (𝜑𝐹 Fn 𝐴)
Assertion
Ref Expression
fnfund (𝜑 → Fun 𝐹)

Proof of Theorem fnfund
StepHypRef Expression
1 fnfund.1 . 2 (𝜑𝐹 Fn 𝐴)
2 fnfun 6603 . 2 (𝐹 Fn 𝐴 → Fun 𝐹)
31, 2syl 17 1 (𝜑 → Fun 𝐹)
Colors of variables: wff setvar class
Syntax hints:  wi 4  Fun wfun 6491   Fn wfn 6492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-an 398  df-fn 6500
This theorem is referenced by:  bnj945  33388  bnj545  33510  bnj548  33512  bnj553  33513  bnj570  33520  bnj929  33551  bnj966  33559  bnj1442  33664  bnj1450  33665  bnj1501  33682  imadrhmcl  40719
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