Theorem dveeq1-o

Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq1 using ax-c11 . (Contributed by NM, 2-Jan-2002) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dveeq1-o	|- ( -. A. x x = y -> ( y = z -> A. x y = z ) )

Proof

Step	Hyp	Ref	Expression
1		ax-5	|- ( w = z -> A. x w = z )
2		ax-5	|- ( y = z -> A. w y = z )
3		equequ1	|- ( w = y -> ( w = z <-> y = z ) )
4	1 2 3	dvelimf-o	|- ( -. A. x x = y -> ( y = z -> A. x y = z ) )