Metamath Proof Explorer


Theorem dveel2

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 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 ) )