Theorem bj-nfs1t2

Description: A theorem close to a closed form of nfs1 . (Contributed by BJ, 2-May-2019)

	Ref	Expression
Assertion	bj-nfs1t2	$$⊢\forall xℲy\phi \to Ⅎx\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		nf5r	$$⊢Ⅎy\phi \to \left(\phi \to \forall y\phi \right)$$
2	1	alimi	$$⊢\forall xℲy\phi \to \forall x\left(\phi \to \forall y\phi \right)$$
3		bj-nfs1t	$$⊢\forall x\left(\phi \to \forall y\phi \right)\to Ⅎx\left[y/x\right]\phi$$
4	2 3	syl	$$⊢\forall xℲy\phi \to Ⅎx\left[y/x\right]\phi$$