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	$$⊢\neg \forall xx=y\to \left(z\in y\to \forall xz\in y\right)$$

Proof

Step	Hyp	Ref	Expression
1		elequ2	$$⊢w=y\to \left(z\in w\leftrightarrow z\in y\right)$$
2	1	dvelimv	$$⊢\neg \forall xx=y\to \left(z\in y\to \forall xz\in y\right)$$