Theorem bj-looinvi 36589

Description: Inference associated with looinv 203. Its associated inference is bj-looinvii 36590. (Contributed by BJ, 30-Mar-2020.)

Hypothesis

Ref	Expression
bj-looinvi.1	⊢ ((𝜑 → 𝜓) → 𝜓)

Assertion

Ref	Expression
bj-looinvi	⊢ ((𝜓 → 𝜑) → 𝜑)

Proof of Theorem bj-looinvi

Step	Hyp	Ref	Expression
1		bj-looinvi.1	. 2 ⊢ ((𝜑 → 𝜓) → 𝜓)
2		looinv 203	. 2 ⊢ (((𝜑 → 𝜓) → 𝜓) → ((𝜓 → 𝜑) → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ((𝜓 → 𝜑) → 𝜑)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  bj-looinvii  36590