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Theorem ffund 5283
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 5282 . 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 5124   -->wf 5126
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-fn 5133  df-f 5134
This theorem is referenced by:  ennnfonelemrnh  11963  ennnfonelemf1  11965  ctinfomlemom  11974  cncnp  12436  txcnp  12477  dvidlemap  12866  dvaddxx  12873  dvmulxx  12874  dvcjbr  12878  dvcj  12879  dvrecap  12883
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