Metamath Proof Explorer

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 ¬ x x = y z y x z y


Step Hyp Ref Expression
1 elequ2 w = y z w z y
2 1 dvelimv ¬ x x = y z y x z y