Theorem fdmi 5544

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 5542	. 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 4776   -->wf 5376

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 5383  df-f 5384

This theorem is used by:  suplocexprlemdisj  8093  suplocexprlemub  8096  eluzel2  9942  inftonninf  10900  qtopbasss  15747  retopbas  15749  tgqioo  15781  dvexp  15937  efcn  15994  pilem3  16010