Theorem elpwi2OLD

Description: Obsolete version of elpwi2 as of 26-May-2024. (Contributed by Glauco Siliprandi, 3-Mar-2021) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	elpwi2.1	⊢ 𝐵 ∈ 𝑉
	elpwi2.2	⊢ 𝐴 ⊆ 𝐵
Assertion	elpwi2OLD	⊢ 𝐴 ∈ 𝒫 𝐵

Proof

Step	Hyp	Ref	Expression
1		elpwi2.1	⊢ 𝐵 ∈ 𝑉
2		elpwi2.2	⊢ 𝐴 ⊆ 𝐵
3		elpw2g	⊢ ( 𝐵 ∈ 𝑉 → ( 𝐴 ∈ 𝒫 𝐵 ↔ 𝐴 ⊆ 𝐵 ) )
4	1 3	ax-mp	⊢ ( 𝐴 ∈ 𝒫 𝐵 ↔ 𝐴 ⊆ 𝐵 )
5	2 4	mpbir	⊢ 𝐴 ∈ 𝒫 𝐵