Theorem 19.23h

Description: Theorem 19.23 of Margaris p. 90. See 19.23 . (Contributed by NM, 24-Jan-1993) (Revised by Mario Carneiro, 24-Sep-2016) (Proof shortened by Wolf Lammen, 1-Jan-2018)

	Ref	Expression
Hypothesis	19.23h.1	$$⊢\psi \to \forall x\psi$$
Assertion	19.23h	$$⊢\forall x\left(\phi \to \psi \right)\leftrightarrow \left(\exists x\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.23h.1	$$⊢\psi \to \forall x\psi$$
2	1	nf5i	$$⊢Ⅎx\psi$$
3	2	19.23	$$⊢\forall x\left(\phi \to \psi \right)\leftrightarrow \left(\exists x\phi \to \psi \right)$$