Theorem elpwOLD

Description: Obsolete proof of elpw as of 31-Dec-2023. (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by NM, 31-Dec-1993)

	Ref	Expression
Hypothesis	elpwOLD.1	⊢ 𝐴 ∈ V
Assertion	elpwOLD	⊢ ( 𝐴 ∈ 𝒫 𝐵 ↔ 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		elpwOLD.1	⊢ 𝐴 ∈ V
2		sseq1	⊢ ( 𝑥 = 𝐴 → ( 𝑥 ⊆ 𝐵 ↔ 𝐴 ⊆ 𝐵 ) )
3		df-pw	⊢ 𝒫 𝐵 = { 𝑥 ∣ 𝑥 ⊆ 𝐵 }
4	1 2 3	elab2	⊢ ( 𝐴 ∈ 𝒫 𝐵 ↔ 𝐴 ⊆ 𝐵 )