Theorem dveeq2

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) (Revised by NM, 20-Jul-2015) Remove dependency on ax-11 . (Revised by Wolf Lammen, 8-Sep-2018) (New usage is discouraged.)

	Ref	Expression
Assertion	dveeq2	$$⊢\neg \forall xx=y\to \left(z=y\to \forall xz=y\right)$$

Proof

Step	Hyp	Ref	Expression
1		nfeqf2	$$⊢\neg \forall xx=y\to Ⅎxz=y$$
2	1	nf5rd	$$⊢\neg \forall xx=y\to \left(z=y\to \forall xz=y\right)$$