Theorem frege12

Description: A closed form of com23 . Proposition 12 of Frege1879 p. 37. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege12	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax-frege8	$$⊢\left(\psi \to \left(\chi \to \theta \right)\right)\to \left(\chi \to \left(\psi \to \theta \right)\right)$$
2		frege5	$$⊢\left(\left(\psi \to \left(\chi \to \theta \right)\right)\to \left(\chi \to \left(\psi \to \theta \right)\right)\right)\to \left(\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)\right)\to \left(\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)\right)$$