Theorem jarli 127

Description: Inference associated with jarl 126. Partial converse of ja 188 (the other partial converse being jarri 108). (Contributed by Wolf Lammen, 4-Oct-2013.)

Hypothesis

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

Assertion

Ref	Expression
jarli	⊢ (¬ 𝜑 → 𝜒)

Proof of Theorem jarli

Step	Hyp	Ref	Expression
1		pm2.21 124	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2		jarli.1	. 2 ⊢ ((𝜑 → 𝜓) → 𝜒)
3	1, 2	syl 18	1 ⊢ (¬ 𝜑 → 𝜒)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  notnotr  131