Theorem con3

Description: Contraposition. Theorem *2.16 of WhiteheadRussell p. 103. This was the fourth axiom of Frege, specifically Proposition 28 of Frege1879 p. 43. Its associated inference is con3i . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 13-Feb-2013)

	Ref	Expression
Assertion	con3	$$⊢\left(\phi \to \psi \right)\to \left(\neg \psi \to \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \to \psi \right)\to \left(\phi \to \psi \right)$$
2	1	con3d	$$⊢\left(\phi \to \psi \right)\to \left(\neg \psi \to \neg \phi \right)$$