Theorem dvelimv

Description: Similar to dvelim with first hypothesis replaced by a distinct variable condition. Usage of this theorem is discouraged because it depends on ax-13 . Check out dvelimhw for a version requiring fewer axioms. (Contributed by NM, 25-Jul-2015) (Proof shortened by Wolf Lammen, 30-Apr-2018) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dvelimv.1	$$⊢z=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	dvelimv	$$⊢\neg \forall xx=y\to \left(\psi \to \forall x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dvelimv.1	$$⊢z=y\to \left(\phi \leftrightarrow \psi \right)$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	2 1	dvelim	$$⊢\neg \forall xx=y\to \left(\psi \to \forall x\psi \right)$$