Theorem con2d

Description: A contraposition deduction. (Contributed by NM, 19-Aug-1993)

	Ref	Expression
Hypothesis	con2d.1	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
Assertion	con2d	$$⊢\phi \to \left(\chi \to \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		con2d.1	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
2		notnotr	$$⊢\neg \neg \psi \to \psi$$
3	2 1	syl5	$$⊢\phi \to \left(\neg \neg \psi \to \neg \chi \right)$$
4	3	con4d	$$⊢\phi \to \left(\chi \to \neg \psi \right)$$