Theorem dveel2

Description: Quantifier introduction when one pair of variables is distinct. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Jan-2002) (New usage is discouraged.)

	Ref	Expression
Assertion	dveel2	|- ( -. A. x x = y -> ( z e. y -> A. x z e. y ) )

Proof

Step	Hyp	Ref	Expression
1		elequ2	|- ( w = y -> ( z e. w <-> z e. y ) )
2	1	dvelimv	|- ( -. A. x x = y -> ( z e. y -> A. x z e. y ) )