Theorem frege17

Description: A closed form of com3l . Proposition 17 of Frege1879 p. 39. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege17	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\psi \to \left(\chi \to \left(\phi \to \theta \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-frege8	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\psi \to \left(\phi \to \left(\chi \to \theta \right)\right)\right)$$
2		frege16	$$⊢\left(\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\psi \to \left(\phi \to \left(\chi \to \theta \right)\right)\right)\right)\to \left(\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\psi \to \left(\chi \to \left(\phi \to \theta \right)\right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\psi \to \left(\chi \to \left(\phi \to \theta \right)\right)\right)$$