Theorem frege40

Description: Anything implies pm2.18 . Proposition 40 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege40	$$⊢\neg \phi \to \left(\left(\neg \psi \to \psi \right)\to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		frege39	$$⊢\left(\neg \psi \to \psi \right)\to \left(\neg \psi \to \phi \right)$$
2		frege35	$$⊢\left(\left(\neg \psi \to \psi \right)\to \left(\neg \psi \to \phi \right)\right)\to \left(\neg \phi \to \left(\left(\neg \psi \to \psi \right)\to \psi \right)\right)$$
3	1 2	ax-mp	$$⊢\neg \phi \to \left(\left(\neg \psi \to \psi \right)\to \psi \right)$$