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	$$⊢F=\left(x\in A,y\in B⟼C\right)$$
Assertion	dmmpogaOLD	$$⊢\forall x\in A\forall y\in BC\in V\to \mathrm{dom}F=A\times B$$

Proof

Step	Hyp	Ref	Expression
1		dmmpog.f	$$⊢F=\left(x\in A,y\in B⟼C\right)$$
2	1	fnmpo	$$⊢\forall x\in A\forall y\in BC\in V\to FFn\left(A\times B\right)$$
3		fndm	$$⊢FFn\left(A\times B\right)\to \mathrm{dom}F=A\times B$$
4	2 3	syl	$$⊢\forall x\in A\forall y\in BC\in V\to \mathrm{dom}F=A\times B$$