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Theorem bnj930 31349
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj930.1 (𝜑𝐹 Fn 𝐴)
Assertion
Ref Expression
bnj930 (𝜑 → Fun 𝐹)

Proof of Theorem bnj930
StepHypRef Expression
1 bnj930.1 . 2 (𝜑𝐹 Fn 𝐴)
2 fnfun 6197 . 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 6093   Fn wfn 6094
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 199  df-an 386  df-fn 6102
This theorem is referenced by:  bnj945  31353  bnj545  31474  bnj548  31476  bnj553  31477  bnj570  31484  bnj929  31515  bnj966  31523  bnj1442  31626  bnj1450  31627  bnj1501  31644
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