Theorem frege13

Description: A closed form of com3r . Proposition 13 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege13	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\chi \to \left(\phi \to \left(\psi \to \theta \right)\right)\right)$$

Proof

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