Theorem ffund 5341

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 5340	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( ph -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5182   -->wf 5184

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 5191  df-f 5192

This theorem is referenced by:  ennnfonelemrnh  12349  ennnfonelemf1  12351  ctinfomlemom  12360  cncnp  12870  txcnp  12911  dvidlemap  13300  dvaddxx  13307  dvmulxx  13308  dvcjbr  13312  dvcj  13313  dvrecap  13317