Theorem dveel1

Description: Quantifier introduction when one pair of variables is disjoint. 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	dveel1	|- ( -. A. x x = y -> ( y e. z -> A. x y e. z ) )

Proof

Step	Hyp	Ref	Expression
1		elequ1	|- ( w = y -> ( w e. z <-> y e. z ) )
2	1	dvelimv	|- ( -. A. x x = y -> ( y e. z -> A. x y e. z ) )