Metamath Proof Explorer


Theorem funfnd

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

Ref Expression
Hypothesis funfnd.1
|- ( ph -> Fun A )
Assertion funfnd
|- ( ph -> A Fn dom A )

Proof

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