Theorem dveeq2-o

Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq2 using ax-c15 . (Contributed by NM, 2-Jan-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dveeq2-o	|- ( -. A. x x = y -> ( z = y -> A. x z = y ) )

Proof

Step	Hyp	Ref	Expression
1		ax-5	|- ( z = w -> A. x z = w )
2		ax-5	|- ( z = y -> A. w z = y )
3		equequ2	|- ( w = y -> ( z = w <-> z = y ) )
4	1 2 3	dvelimf-o	|- ( -. A. x x = y -> ( z = y -> A. x z = y ) )