Theorem fdmi 5541

Description: The domain of a mapping. (Contributed by NM, 28-Jul-2008.)

Hypothesis

Ref	Expression
fdmi.1	|- F : A --> B

Assertion

Ref	Expression
fdmi	|- dom F = A

Proof of Theorem fdmi

Step	Hyp	Ref	Expression
1		fdmi.1	. 2 |- F : A --> B
2		fdm 5539	. 2 |- ( F : A --> B -> dom F = A )
3	1, 2	ax-mp 5	1 |- dom F = A

This proof depends on syntax axioms:   = wceq 1402   dom cdm 4774   -->wf 5373

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  df-f 5381

This theorem is used by:  suplocexprlemdisj  8087  suplocexprlemub  8090  eluzel2  9926  inftonninf  10879  qtopbasss  15622  retopbas  15624  tgqioo  15656  dvexp  15812  efcn  15869  pilem3  15884