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 → 𝐴 ∈ 𝒫 𝐵 )
Assertion	elpwid	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		elpwid.1	⊢ ( 𝜑 → 𝐴 ∈ 𝒫 𝐵 )
2		elpwi	⊢ ( 𝐴 ∈ 𝒫 𝐵 → 𝐴 ⊆ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )