Theorem ffund 5407

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

Step	Hyp	Ref	Expression
1		ffund.1	. 2 |- ( ph -> F : A --> B )
2		ffun 5406	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( ph -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5248   -->wf 5250

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 5257  df-f 5258

This theorem is referenced by:  ennnfonelemrnh  12573  ennnfonelemf1  12575  ctinfomlemom  12584  psrbaglesuppg  14158  psrelbasfun  14161  cncnp  14398  txcnp  14439  dvidlemap  14845  dvaddxx  14852  dvmulxx  14853  dvcjbr  14857  dvcj  14858  dvrecap  14862  plyaddlem1  14893  plymullem1  14894