Theorem 19.23

Description: Theorem 19.23 of Margaris p. 90. See 19.23v for a version requiring fewer axioms. (Contributed by NM, 24-Jan-1993) (Revised by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypothesis	19.23.1	$$⊢Ⅎx\psi$$
Assertion	19.23	$$⊢\forall x\left(\phi \to \psi \right)\leftrightarrow \left(\exists x\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.23.1	$$⊢Ⅎx\psi$$
2		19.23t	$$⊢Ⅎx\psi \to \left(\forall x\left(\phi \to \psi \right)\leftrightarrow \left(\exists x\phi \to \psi \right)\right)$$
3	1 2	ax-mp	$$⊢\forall x\left(\phi \to \psi \right)\leftrightarrow \left(\exists x\phi \to \psi \right)$$