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Theorem ffund 5364
Description: A mapping is a function, deduction version. (Contributed by Glauco Siliprandi, 3-Mar-2021.)
Hypothesis
Ref Expression
ffund.1  |-  ( ph  ->  F : A --> B )
Assertion
Ref Expression
ffund  |-  ( ph  ->  Fun  F )

Proof of Theorem ffund
StepHypRef Expression
1 ffund.1 . 2  |-  ( ph  ->  F : A --> B )
2 ffun 5363 . 2  |-  ( F : A --> B  ->  Fun  F )
31, 2syl 14 1  |-  ( ph  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5205   -->wf 5207
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106
This theorem depends on definitions:  df-bi 117  df-fn 5214  df-f 5215
This theorem is referenced by:  ennnfonelemrnh  12387  ennnfonelemf1  12389  ctinfomlemom  12398  cncnp  13363  txcnp  13404  dvidlemap  13793  dvaddxx  13800  dvmulxx  13801  dvcjbr  13805  dvcj  13806  dvrecap  13810
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