Theorem fndmd 39441

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 5990	. 2 |- ( F Fn A -> dom F = A )
3	1, 2	syl 17	1 |- ( ph -> dom F = A )

Syntax hints:   -> wi 4   = wceq 1483   dom cdm 5114   Fn wfn 5883

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-fn 5891

This theorem is referenced by:  fvelimad  39458  fnfvimad  39459  limsupequzlem  39954  climrescn  39980  smflimmpt  41016  smflimsuplem7  41032