Theorem elpmi2

Description: The domain of a partial function. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Assertion	elpmi2	⊢ ( 𝐹 ∈ ( 𝐴 ↑pm 𝐵 ) → dom 𝐹 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		elpmi	⊢ ( 𝐹 ∈ ( 𝐴 ↑pm 𝐵 ) → ( 𝐹 : dom 𝐹 ⟶ 𝐴 ∧ dom 𝐹 ⊆ 𝐵 ) )
2	1	simprd	⊢ ( 𝐹 ∈ ( 𝐴 ↑pm 𝐵 ) → dom 𝐹 ⊆ 𝐵 )