Theorem frege16

Description: A closed form of com34 . Proposition 16 of Frege1879 p. 38. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege16	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)\right)\to \left(\phi \to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		frege12	$$⊢\left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)\to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)$$
2		frege5	$$⊢\left(\left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)\to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)\right)\to \left(\left(\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)\right)\to \left(\phi \to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)\right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)\right)\to \left(\phi \to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)\right)$$