Theorem fndmd 5438

Description: The domain of a function. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Hypothesis

Ref	Expression
fndmd.1	|- ( ph -> F Fn A )

Assertion

Ref	Expression
fndmd	|- ( ph -> dom F = A )

Proof of Theorem fndmd

Step	Hyp	Ref	Expression
1		fndmd.1	. 2 |- ( ph -> F Fn A )
2		fndm 5436	. 2 |- ( F Fn A -> dom F = A )
3	1, 2	syl 14	1 |- ( ph -> dom F = A )

Syntax hints:   -> wi 4   = wceq 1398   dom cdm 4731   Fn wfn 5328

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem depends on definitions:  df-bi 117  df-fn 5336

This theorem is referenced by:  fndmexd  5534  prdsbas2  13423  prdsplusgval  13427  prdsmulrval  13429  edgstruct  15985