Theorem con1

Description: Contraposition. Theorem *2.15 of WhiteheadRussell p. 102. Its associated inference is con1i . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 12-Feb-2013)

	Ref	Expression
Assertion	con1	$$⊢\left(\neg \phi \to \psi \right)\to \left(\neg \psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\neg \phi \to \psi \right)\to \left(\neg \phi \to \psi \right)$$
2	1	con1d	$$⊢\left(\neg \phi \to \psi \right)\to \left(\neg \psi \to \phi \right)$$