Theorem 19.9ht

Description: A closed version of 19.9h . (Contributed by NM, 13-May-1993) (Proof shortened by Wolf Lammen, 3-Mar-2018)

	Ref	Expression
Assertion	19.9ht	$$⊢\forall x\left(\phi \to \forall x\phi \right)\to \left(\exists x\phi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nf5-1	$$⊢\forall x\left(\phi \to \forall x\phi \right)\to Ⅎx\phi$$
2	1	19.9d	$$⊢\forall x\left(\phi \to \forall x\phi \right)\to \left(\exists x\phi \to \phi \right)$$