Theorem ax3h

Description: Recover ax-3 from hirstL-ax3 . (Contributed by Jarvin Udandy, 3-Jul-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	ax3h	$$⊢\left(\neg \phi \to \neg \psi \right)\to \left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		hirstL-ax3	$$⊢\left(\neg \phi \to \neg \psi \right)\to \left(\left(\neg \phi \to \psi \right)\to \phi \right)$$
2		jarr	$$⊢\left(\left(\neg \phi \to \psi \right)\to \phi \right)\to \left(\psi \to \phi \right)$$
3	1 2	syl	$$⊢\left(\neg \phi \to \neg \psi \right)\to \left(\psi \to \phi \right)$$