Theorem dmmpogaOLD

Description: Obsolete version of dmmpoga as of 29-May-2024. (Contributed by Alexander van der Vekens, 10-Feb-2019) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	dmmpog.f	|- F = ( x e. A , y e. B |-> C )
Assertion	dmmpogaOLD	|- ( A. x e. A A. y e. B C e. V -> dom F = ( A X. B ) )

Proof

Step	Hyp	Ref	Expression
1		dmmpog.f	|- F = ( x e. A , y e. B |-> C )
2	1	fnmpo	|- ( A. x e. A A. y e. B C e. V -> F Fn ( A X. B ) )
3		fndm	|- ( F Fn ( A X. B ) -> dom F = ( A X. B ) )
4	2 3	syl	|- ( A. x e. A A. y e. B C e. V -> dom F = ( A X. B ) )