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 e. B -> { A } e. ~P B )

Proof

Step	Hyp	Ref	Expression
1		snelpwg	|- ( A e. B -> ( A e. B <-> { A } e. ~P B ) )
2	1	ibi	|- ( A e. B -> { A } e. ~P B )