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	⊢ ( ( 𝜑 → 𝜓 ) → 𝜓 )
Assertion	bj-looinvi	⊢ ( ( 𝜓 → 𝜑 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bj-looinvi.1	⊢ ( ( 𝜑 → 𝜓 ) → 𝜓 )
2		looinv	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜓 ) → ( ( 𝜓 → 𝜑 ) → 𝜑 ) )
3	1 2	ax-mp	⊢ ( ( 𝜓 → 𝜑 ) → 𝜑 )