Theorem fdmi 5516

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 5514	. 2 |- ( F : A --> B -> dom F = A )
3	1, 2	ax-mp 5	1 |- dom F = A

Syntax hints:   = wceq 1398   dom cdm 4749   -->wf 5348

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 5355  df-f 5356

This theorem is referenced by:  suplocexprlemdisj  8035  suplocexprlemub  8038  eluzel2  9858  inftonninf  10804  qtopbasss  15386  retopbas  15388  tgqioo  15420  dvexp  15576  efcn  15633  pilem3  15648