Theorem fdmi 5412

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 5410	. 2 |- ( F : A --> B -> dom F = A )
3	1, 2	ax-mp 5	1 |- dom F = A

Syntax hints:   = wceq 1364   dom cdm 4660   -->wf 5251

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 5258  df-f 5259

This theorem is referenced by:  suplocexprlemdisj  7782  suplocexprlemub  7785  eluzel2  9600  inftonninf  10516  qtopbasss  14700  retopbas  14702  tgqioo  14734  dvexp  14890  efcn  14944  pilem3  14959