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	$$⊢A\in B\to \left\{A\right\}\in 𝒫B$$

Proof

Step	Hyp	Ref	Expression
1		snelpwg	$$⊢A\in B\to \left(A\in B\leftrightarrow \left\{A\right\}\in 𝒫B\right)$$
2	1	ibi	$$⊢A\in B\to \left\{A\right\}\in 𝒫B$$