Theorem com15

Description: Commutation of antecedents. Swap 1st and 5th. (Contributed by Jeff Hankins, 28-Jun-2009) (Proof shortened by Wolf Lammen, 29-Jul-2012)

	Ref	Expression
Hypothesis	com5.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$
Assertion	com15	$$⊢\tau \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\phi \to \eta \right)\right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		com5.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)\right)\right)$$
2	1	com5l	$$⊢\psi \to \left(\chi \to \left(\theta \to \left(\tau \to \left(\phi \to \eta \right)\right)\right)\right)$$
3	2	com4r	$$⊢\tau \to \left(\psi \to \left(\chi \to \left(\theta \to \left(\phi \to \eta \right)\right)\right)\right)$$