Theorem unipwr

Description: A class is a subclass of the union of its power class. This theorem is the right-to-left subclass lemma of unipw . The proof of this theorem was automatically generated from unipwrVD using a tools command file , translateMWO.cmd , by translating the proof into its non-virtual deduction form and minimizing it. (Contributed by Alan Sare, 25-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	unipwr	|- A C_ U. ~P A

Proof

Step	Hyp	Ref	Expression
1		vex	|- x e. _V
2	1	snid	|- x e. { x }
3		snelpwi	|- ( x e. A -> { x } e. ~P A )
4		elunii	|- ( ( x e. { x } /\ { x } e. ~P A ) -> x e. U. ~P A )
5	2 3 4	sylancr	|- ( x e. A -> x e. U. ~P A )
6	5	ssriv	|- A C_ U. ~P A