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	$$⊢A\in \mathrm{V}$$
Assertion	elpwOLD	$$⊢A\in 𝒫B\leftrightarrow A\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		elpwOLD.1	$$⊢A\in \mathrm{V}$$
2		sseq1	$$⊢x=A\to \left(x\subseteq B\leftrightarrow A\subseteq B\right)$$
3		df-pw	$$⊢𝒫B=\left\{x|x\subseteq B\right\}$$
4	1 2 3	elab2	$$⊢A\in 𝒫B\leftrightarrow A\subseteq B$$