Theorem impi

Description: An importation inference. (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 20-Jul-2013)

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

Proof

Step	Hyp	Ref	Expression
1		impi.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	con3rr3	⊢ ( ¬ 𝜒 → ( 𝜑 → ¬ 𝜓 ) )
3	2	con1i	⊢ ( ¬ ( 𝜑 → ¬ 𝜓 ) → 𝜒 )