Theorem com24

Description: Commutation of antecedents. Swap 2nd and 4th. Deduction associated with com13 . (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)

	Ref	Expression
Hypothesis	com4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
Assertion	com24	$$⊢\phi \to \left(\theta \to \left(\chi \to \left(\psi \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		com4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
2	1	com4t	$$⊢\chi \to \left(\theta \to \left(\phi \to \left(\psi \to \tau \right)\right)\right)$$
3	2	com13	$$⊢\phi \to \left(\theta \to \left(\chi \to \left(\psi \to \tau \right)\right)\right)$$