Theorem 19.36imvOLD

Description: Obsolete version of 19.36imv as of 22-Sep-2024. (Contributed by Rohan Ridenour, 16-Apr-2022) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	19.36imvOLD	$$⊢\exists x\left(\phi \to \psi \right)\to \left(\forall x\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		19.35	$$⊢\exists x\left(\phi \to \psi \right)\leftrightarrow \left(\forall x\phi \to \exists x\psi \right)$$
2	1	biimpi	$$⊢\exists x\left(\phi \to \psi \right)\to \left(\forall x\phi \to \exists x\psi \right)$$
3		ax5e	$$⊢\exists x\psi \to \psi$$
4	2 3	syl6	$$⊢\exists x\left(\phi \to \psi \right)\to \left(\forall x\phi \to \psi \right)$$