Theorem fdmi 5228

Description: The domain of a mapping. (Contributed by set.mm contributors, 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 5227	. 2 |- (F:A-->B -> dom F = A)
3	1, 2	ax-mp 5	1 |- dom F = A

This proof depends on syntax axioms:   = wceq 1642  dom cdm 4773  -->wf 4778

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-fn 4791  df-f 4792

This theorem is used by:  f0cli  5419