Theorem bj-nfdt0

Description: A theorem close to a closed form of nf5d and nf5dh . (Contributed by BJ, 2-May-2019)

	Ref	Expression
Assertion	bj-nfdt0	$$⊢\forall x\left(\phi \to \left(\psi \to \forall x\psi \right)\right)\to \left(\forall x\phi \to Ⅎx\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		alim	$$⊢\forall x\left(\phi \to \left(\psi \to \forall x\psi \right)\right)\to \left(\forall x\phi \to \forall x\left(\psi \to \forall x\psi \right)\right)$$
2		nf5	$$⊢Ⅎx\psi \leftrightarrow \forall x\left(\psi \to \forall x\psi \right)$$
3	1 2	imbitrrdi	$$⊢\forall x\left(\phi \to \left(\psi \to \forall x\psi \right)\right)\to \left(\forall x\phi \to Ⅎx\psi \right)$$