Theorem bj-looinvi

Description: Inference associated with looinv . Its associated inference is bj-looinvii . (Contributed by BJ, 30-Mar-2020)

	Ref	Expression
Hypothesis	bj-looinvi.1	$$⊢\left(\phi \to \psi \right)\to \psi$$
Assertion	bj-looinvi	$$⊢\left(\psi \to \phi \right)\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		bj-looinvi.1	$$⊢\left(\phi \to \psi \right)\to \psi$$
2		looinv	$$⊢\left(\left(\phi \to \psi \right)\to \psi \right)\to \left(\left(\psi \to \phi \right)\to \phi \right)$$
3	1 2	ax-mp	$$⊢\left(\psi \to \phi \right)\to \phi$$