Theorem bj-looinvii 34748

Description: Inference associated with bj-looinvi 34747. (Contributed by BJ, 30-Mar-2020.)

Hypotheses

Ref	Expression
bj-looinvii.1	⊢ ((𝜑 → 𝜓) → 𝜓)
bj-looinvii.2	⊢ (𝜓 → 𝜑)

Assertion

Ref	Expression
bj-looinvii	⊢ 𝜑

Proof of Theorem bj-looinvii

Step	Hyp	Ref	Expression
1		bj-looinvii.2	. 2 ⊢ (𝜓 → 𝜑)
2		bj-looinvii.1	. . 3 ⊢ ((𝜑 → 𝜓) → 𝜓)
3	2	bj-looinvi 34747	. 2 ⊢ ((𝜓 → 𝜑) → 𝜑)
4	1, 3	ax-mp 5	1 ⊢ 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: (None)