Theorem snelpwi

Description: If a set is a member of a class, then the singleton of that set is a member of the powerclass of that class. (Contributed by Alan Sare, 25-Aug-2011)

	Ref	Expression
Assertion	snelpwi	⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ∈ 𝒫 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		snelpwg	⊢ ( 𝐴 ∈ 𝐵 → ( 𝐴 ∈ 𝐵 ↔ { 𝐴 } ∈ 𝒫 𝐵 ) )
2	1	ibi	⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ∈ 𝒫 𝐵 )