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Theorem bnj930 29900
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 5888 . 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 5784   Fn wfn 5785
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 195  df-an 384  df-fn 5793
This theorem is referenced by:  bnj945  29904  bnj545  30025  bnj548  30027  bnj553  30028  bnj570  30035  bnj929  30066  bnj966  30074  bnj1442  30177  bnj1450  30178  bnj1501  30195
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