Theorem elpm2

Description: The predicate "is a partial function." (Contributed by NM, 15-Nov-2007) (Revised by Mario Carneiro, 31-Dec-2013)

	Ref	Expression
Hypotheses	elmap.1	|- A e. _V
	elmap.2	|- B e. _V
Assertion	elpm2	|- ( F e. ( A ^pm B ) <-> ( F : dom F --> A /\ dom F C_ B ) )

Proof

Step	Hyp	Ref	Expression
1		elmap.1	|- A e. _V
2		elmap.2	|- B e. _V
3		elpm2g	|- ( ( A e. _V /\ B e. _V ) -> ( F e. ( A ^pm B ) <-> ( F : dom F --> A /\ dom F C_ B ) ) )
4	1 2 3	mp2an	|- ( F e. ( A ^pm B ) <-> ( F : dom F --> A /\ dom F C_ B ) )