Theorem bj-nfdt

Description: Closed form of nf5d and nf5dh . (Contributed by BJ, 2-May-2019)

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

Proof

Step	Hyp	Ref	Expression
1		bj-nfdt0	$$⊢\forall x\left(\phi \to \left(\psi \to \forall x\psi \right)\right)\to \left(\forall x\phi \to Ⅎx\psi \right)$$
2	1	imim2d	$$⊢\forall x\left(\phi \to \left(\psi \to \forall x\psi \right)\right)\to \left(\left(\phi \to \forall x\phi \right)\to \left(\phi \to Ⅎx\psi \right)\right)$$