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Metamath Proof Explorer

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	$⊢ φ \to A \in 𝒫 B$
	Assertion	elpwid	$⊢ φ \to A \subseteq B$

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