Theorem jarri 107

Description: Inference associated with jarr 106. Partial converse of ja 186 (the other partial converse being jarli 126). (Contributed by Wolf Lammen, 20-Sep-2013.)

Hypothesis

Ref	Expression
jarri.1	⊢ ((𝜑 → 𝜓) → 𝜒)

Assertion

Ref	Expression
jarri	⊢ (𝜓 → 𝜒)

Proof of Theorem jarri

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜓 → (𝜑 → 𝜓))
2		jarri.1	. 2 ⊢ ((𝜑 → 𝜓) → 𝜒)
3	1, 2	syl 17	1 ⊢ (𝜓 → 𝜒)

Syntax hints:   → wi 4

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

This theorem is referenced by:  pm2.86i  110  dedlem0a  1044