Theorem tsksn

Description: A singleton of an element of a Tarski class belongs to the class. JFM CLASSES2 th. 2 (partly). (Contributed by FL, 22-Feb-2011) (Revised by Mario Carneiro, 18-Jun-2013)

	Ref	Expression
Assertion	tsksn	|- ( ( T e. Tarski /\ A e. T ) -> { A } e. T )

Proof

Step	Hyp	Ref	Expression
1		tskpw	|- ( ( T e. Tarski /\ A e. T ) -> ~P A e. T )
2		snsspw	|- { A } C_ ~P A
3		tskss	|- ( ( T e. Tarski /\ ~P A e. T /\ { A } C_ ~P A ) -> { A } e. T )
4	2 3	mp3an3	|- ( ( T e. Tarski /\ ~P A e. T ) -> { A } e. T )
5	1 4	syldan	|- ( ( T e. Tarski /\ A e. T ) -> { A } e. T )