Theorem funfnd 5219

Description: A function is a function over its domain. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Hypothesis

Ref	Expression
funfnd.1	|- ( ph -> Fun A )

Assertion

Ref	Expression
funfnd	|- ( ph -> A Fn dom A )

Proof of Theorem funfnd

Step	Hyp	Ref	Expression
1		funfnd.1	. 2 |- ( ph -> Fun A )
2		funfn 5218	. 2 |- ( Fun A <-> A Fn dom A )
3	1, 2	sylib 121	1 |- ( ph -> A Fn dom A )

Syntax hints:   -> wi 4   dom cdm 4604   Fun wfun 5182   Fn wfn 5183

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1437  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-cleq 2158  df-fn 5191

This theorem is referenced by:  ennnfonelemf1  12351  dvfgg  13307