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Theorem bnj930 29202
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 5544 . 2  |-  ( F  Fn  A  ->  Fun  F )
31, 2syl 16 1  |-  ( ph  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5450    Fn wfn 5451
This theorem is referenced by:  bnj945  29206  bnj545  29328  bnj548  29330  bnj553  29331  bnj570  29338  bnj929  29369  bnj966  29377  bnj1442  29480  bnj1450  29481  bnj1501  29498
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 179  df-an 362  df-fn 5459
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