Theorem frege44

Description: Similar to a commuted pm2.62 . Proposition 44 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege44	$$⊢\left(\neg \phi \to \psi \right)\to \left(\left(\psi \to \phi \right)\to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		frege43	$$⊢\left(\neg \phi \to \phi \right)\to \phi$$
2		frege21	$$⊢\left(\left(\neg \phi \to \phi \right)\to \phi \right)\to \left(\left(\neg \phi \to \psi \right)\to \left(\left(\psi \to \phi \right)\to \phi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\neg \phi \to \psi \right)\to \left(\left(\psi \to \phi \right)\to \phi \right)$$