Theorem fdmi 5280

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 5278	. 2 |- ( F : A --> B -> dom F = A )
3	1, 2	ax-mp 5	1 |- dom F = A

Syntax hints:   = wceq 1331   dom cdm 4539   -->wf 5119

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-fn 5126  df-f 5127

This theorem is referenced by:  suplocexprlemdisj  7528  suplocexprlemub  7531  eluzel2  9331  inftonninf  10214  qtopbasss  12690  retopbas  12692  tgqioo  12716  dvexp  12844  efcn  12857  pilem3  12864