Theorem frege39

Description: Syllogism between pm2.18 and pm2.24 . Proposition 39 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege39	$$⊢\left(\neg \phi \to \phi \right)\to \left(\neg \phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		frege38	$$⊢\neg \phi \to \left(\phi \to \psi \right)$$
2		ax-frege2	$$⊢\left(\neg \phi \to \left(\phi \to \psi \right)\right)\to \left(\left(\neg \phi \to \phi \right)\to \left(\neg \phi \to \psi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\neg \phi \to \phi \right)\to \left(\neg \phi \to \psi \right)$$