Theorem elpwid

Description: An element of a power class is a subclass. Deduction form of elpwi . (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypothesis	elpwid.1	$$⊢\phi \to A\in 𝒫B$$
Assertion	elpwid	$$⊢\phi \to A\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		elpwid.1	$$⊢\phi \to A\in 𝒫B$$
2		elpwi	$$⊢A\in 𝒫B\to A\subseteq B$$
3	1 2	syl	$$⊢\phi \to A\subseteq B$$