Theorem fndmi 5481

Description: The domain of a function. (Contributed by Wolf Lammen, 1-Jun-2024.)

Hypothesis

Ref	Expression
fndmi.1	|- F Fn A

Assertion

Ref	Expression
fndmi	|- dom F = A

Proof of Theorem fndmi

Step	Hyp	Ref	Expression
1		fndmi.1	. 2 |- F Fn A
2		fndm 5480	. 2 |- ( F Fn A -> dom F = A )
3	1, 2	ax-mp 5	1 |- dom F = A

This proof depends on syntax axioms:   = 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:  pfxclz  11453