Theorem snelpw

Description: A singleton of a set is a member of the powerclass of a class if and only if that set is a member of that class. (Contributed by NM, 1-Apr-1998)

	Ref	Expression
Hypothesis	snelpw.ex	|- A e. _V
Assertion	snelpw	|- ( A e. B <-> { A } e. ~P B )

Proof

Step	Hyp	Ref	Expression
1		snelpw.ex	|- A e. _V
2		snelpwg	|- ( A e. _V -> ( A e. B <-> { A } e. ~P B ) )
3	1 2	ax-mp	|- ( A e. B <-> { A } e. ~P B )