Theorem bj-jarrii 34657

Description: Inference associated with jarri 107. Contrary to it , it does not require ax-2 7, but only ax-mp 5 and ax-1 6. (Contributed by BJ, 29-Mar-2020.) (Proof modification is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
bj-jarrii	⊢ 𝜒

Proof of Theorem bj-jarrii

Step	Hyp	Ref	Expression
1		bj-jarrii.2	. . 3 ⊢ 𝜓
2	1	a1i 11	. 2 ⊢ (𝜑 → 𝜓)
3		bj-jarrii.1	. 2 ⊢ ((𝜑 → 𝜓) → 𝜒)
4	2, 3	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6

This theorem is referenced by: (None)