Theorem pwuninel2

Description: Proof of pwuninel under the assumption that the union of the given class is a set, avoiding ax-pr and ax-un . (Contributed by Stefan O'Rear, 22-Feb-2015)

	Ref	Expression
Assertion	pwuninel2	|- ( U. A e. V -> -. ~P U. A e. A )

Proof

Step	Hyp	Ref	Expression
1		pwnss	|- ( U. A e. V -> -. ~P U. A C_ U. A )
2		elssuni	|- ( ~P U. A e. A -> ~P U. A C_ U. A )
3	1 2	nsyl	|- ( U. A e. V -> -. ~P U. A e. A )