Theorem fndmd 5482

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 5480	. 2 |- ( F Fn A -> dom F = A )
3	1, 2	syl 14	1 |- ( ph -> dom F = A )

This proof depends on syntax axioms:   -> wi 4   = wceq 1402   dom cdm 4774   Fn wfn 5372

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This proof depends on definitions:  df-bi 117  df-fn 5380

This theorem is used by:  fndmexd  5581  prdsbas2  14181  prdsplusgval  14185  prdsmulrval  14187  edgstruct  16317