Theorem ffdm

Description: A mapping is a partial function. (Contributed by NM, 25-Nov-2007)

	Ref	Expression
Assertion	ffdm	|- ( F : A --> B -> ( F : dom F --> B /\ dom F C_ A ) )

Proof

Step	Hyp	Ref	Expression
1		fdm	|- ( F : A --> B -> dom F = A )
2	1	feq2d	|- ( F : A --> B -> ( F : dom F --> B <-> F : A --> B ) )
3	2	ibir	|- ( F : A --> B -> F : dom F --> B )
4		eqimss	|- ( dom F = A -> dom F C_ A )
5	1 4	syl	|- ( F : A --> B -> dom F C_ A )
6	3 5	jca	|- ( F : A --> B -> ( F : dom F --> B /\ dom F C_ A ) )