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	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	impi	$$⊢\neg \left(\phi \to \neg \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		impi.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	con3rr3	$$⊢\neg \chi \to \left(\phi \to \neg \psi \right)$$
3	2	con1i	$$⊢\neg \left(\phi \to \neg \psi \right)\to \chi$$