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Theorem bnj930 29117
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj930.1  |-  ( ph  ->  F  Fn  A )
Assertion
Ref Expression
bnj930  |-  ( ph  ->  Fun  F )

Proof of Theorem bnj930
StepHypRef Expression
1 bnj930.1 . 2  |-  ( ph  ->  F  Fn  A )
2 fnfun 5357 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 15 1  |-  ( ph  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5265    Fn wfn 5266
This theorem is referenced by:  bnj945  29121  bnj545  29243  bnj548  29245  bnj553  29246  bnj570  29253  bnj929  29284  bnj966  29292  bnj1442  29395  bnj1450  29396  bnj1501  29413
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-fn 5274
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