Theorem con1d

Description: A contraposition deduction. (Contributed by NM, 27-Dec-1992)

	Ref	Expression
Hypothesis	con1d.1	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
Assertion	con1d	$$⊢\phi \to \left(\neg \chi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		con1d.1	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
2		notnot	$$⊢\chi \to \neg \neg \chi$$
3	1 2	syl6	$$⊢\phi \to \left(\neg \psi \to \neg \neg \chi \right)$$
4	3	con4d	$$⊢\phi \to \left(\neg \chi \to \psi \right)$$