Theorem 19.3t

Description: Closed form of 19.3 and version of 19.9t with a universal quantifier. (Contributed by NM, 9-Nov-2020) (Proof shortened by BJ, 9-Oct-2022)

	Ref	Expression
Assertion	19.3t	$$⊢Ⅎx\phi \to \left(\forall x\phi \leftrightarrow \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sp	$$⊢\forall x\phi \to \phi$$
2		nf5r	$$⊢Ⅎx\phi \to \left(\phi \to \forall x\phi \right)$$
3	1 2	impbid2	$$⊢Ⅎx\phi \to \left(\forall x\phi \leftrightarrow \phi \right)$$