Theorem jarli

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

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

Proof

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