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

Proof

Step	Hyp	Ref	Expression
1		elequ1	$$⊢w=y\to \left(w\in z\leftrightarrow y\in z\right)$$
2	1	dvelimv	$$⊢\neg \forall xx=y\to \left(y\in z\to \forall xy\in z\right)$$