Theorem frege35

Description: Commuted, closed form of con1d . Proposition 35 of Frege1879 p. 45. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege35	$$⊢\left(\phi \to \left(\neg \psi \to \chi \right)\right)\to \left(\neg \chi \to \left(\phi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		frege34	$$⊢\left(\phi \to \left(\neg \psi \to \chi \right)\right)\to \left(\phi \to \left(\neg \chi \to \psi \right)\right)$$
2		frege12	$$⊢\left(\left(\phi \to \left(\neg \psi \to \chi \right)\right)\to \left(\phi \to \left(\neg \chi \to \psi \right)\right)\right)\to \left(\left(\phi \to \left(\neg \psi \to \chi \right)\right)\to \left(\neg \chi \to \left(\phi \to \psi \right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \left(\neg \psi \to \chi \right)\right)\to \left(\neg \chi \to \left(\phi \to \psi \right)\right)$$