Theorem 19.36i

Description: Inference associated with 19.36 . See 19.36iv for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993)

	Ref	Expression
Hypotheses	19.36.1	$$⊢Ⅎx\psi$$
	19.36i.2	$$⊢\exists x\left(\phi \to \psi \right)$$
Assertion	19.36i	$$⊢\forall x\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		19.36.1	$$⊢Ⅎx\psi$$
2		19.36i.2	$$⊢\exists x\left(\phi \to \psi \right)$$
3	1	19.36	$$⊢\exists x\left(\phi \to \psi \right)\leftrightarrow \left(\forall x\phi \to \psi \right)$$
4	2 3	mpbi	$$⊢\forall x\phi \to \psi$$