Theorem dmmpoga

Description: Domain of an operation given by the maps-to notation, closed form of dmmpo . (Contributed by Alexander van der Vekens, 10-Feb-2019) (Proof shortened by Lammen, 29-May-2024)

	Ref	Expression
Hypothesis	dmmpog.f	|- F = ( x e. A , y e. B |-> C )
Assertion	dmmpoga	|- ( 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	2	fndmd	|- ( A. x e. A A. y e. B C e. V -> dom F = ( A X. B ) )