Theorem dmmpo

Description: Domain of a class given by the maps-to notation. (Contributed by FL, 17-May-2010)

	Ref	Expression
Hypotheses	fmpo.1	⊢ 𝐹 = ( 𝑥 ∈ 𝐴 , 𝑦 ∈ 𝐵 ↦ 𝐶 )
	fnmpoi.2	⊢ 𝐶 ∈ V
Assertion	dmmpo	⊢ dom 𝐹 = ( 𝐴 × 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		fmpo.1	⊢ 𝐹 = ( 𝑥 ∈ 𝐴 , 𝑦 ∈ 𝐵 ↦ 𝐶 )
2		fnmpoi.2	⊢ 𝐶 ∈ V
3	1 2	fnmpoi	⊢ 𝐹 Fn ( 𝐴 × 𝐵 )
4	3	fndmi	⊢ dom 𝐹 = ( 𝐴 × 𝐵 )