Theorem fdmi 5375

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 5373	. 2 |- ( F : A --> B -> dom F = A )
3	1, 2	ax-mp 5	1 |- dom F = A

Syntax hints:   = wceq 1353   dom cdm 4628   -->wf 5214

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 5221  df-f 5222

This theorem is referenced by:  suplocexprlemdisj  7721  suplocexprlemub  7724  eluzel2  9535  inftonninf  10443  qtopbasss  14060  retopbas  14062  tgqioo  14086  dvexp  14214  efcn  14228  pilem3  14243