Theorem elpwi

Description: Subset relation implied by membership in a power class. (Contributed by NM, 17-Feb-2007)

	Ref	Expression
Assertion	elpwi	⊢ ( 𝐴 ∈ 𝒫 𝐵 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		elpwg	⊢ ( 𝐴 ∈ 𝒫 𝐵 → ( 𝐴 ∈ 𝒫 𝐵 ↔ 𝐴 ⊆ 𝐵 ) )
2	1	ibi	⊢ ( 𝐴 ∈ 𝒫 𝐵 → 𝐴 ⊆ 𝐵 )