Theorem bj-dvelimv

Description: A version of dvelim using the "nonfree" idiom. (Contributed by BJ, 20-Oct-2021) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-dvelimv.nf	$$⊢Ⅎx\psi$$
	bj-dvelimv.is	$$⊢z=y\to \left(\psi \leftrightarrow \phi \right)$$
Assertion	bj-dvelimv	$$⊢\neg \forall xx=y\to Ⅎx\phi$$

Proof

Step	Hyp	Ref	Expression
1		bj-dvelimv.nf	$$⊢Ⅎx\psi$$
2		bj-dvelimv.is	$$⊢z=y\to \left(\psi \leftrightarrow \phi \right)$$
3	1	a1i	$$⊢\top \to Ⅎx\psi$$
4	3 2	bj-dvelimdv1	$$⊢\top \to \left(\neg \forall xx=y\to Ⅎx\phi \right)$$
5	4	mptru	$$⊢\neg \forall xx=y\to Ⅎx\phi$$