Theorem elpm

Description: The predicate "is a partial function". (Contributed by NM, 15-Nov-2007) (Revised by Mario Carneiro, 14-Nov-2013)

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

Proof

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