Theorem fdmi 5227

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 5226	. 2 ⊢ (F:A–→B → dom F = A)
3	1, 2	ax-mp 5	1 ⊢ dom F = A

Syntax hints:   = wceq 1642  dom cdm 4772  –→wf 4777

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-fn 4790  df-f 4791

This theorem is referenced by:  f0cli  5418