Theorem com25

Description: Commutation of antecedents. Swap 2nd and 5th. Deduction associated with com14 . (Contributed by Jeff Hankins, 28-Jun-2009)

	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	com25	$$⊢\phi \to \left(\tau \to \left(\chi \to \left(\theta \to \left(\psi \to \eta \right)\right)\right)\right)$$

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	com24	$$⊢\phi \to \left(\theta \to \left(\chi \to \left(\psi \to \left(\tau \to \eta \right)\right)\right)\right)$$
3	2	com45	$$⊢\phi \to \left(\theta \to \left(\chi \to \left(\tau \to \left(\psi \to \eta \right)\right)\right)\right)$$
4	3	com24	$$⊢\phi \to \left(\tau \to \left(\chi \to \left(\theta \to \left(\psi \to \eta \right)\right)\right)\right)$$