Theorem com45

Description: Commutation of antecedents. Swap 4th and 5th. Deduction associated with com34 . Double deduction associated with com23 . Triple deduction associated with com12 . (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	com45	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\tau \to \left(\theta \to \eta \right)\right)\right)\right)$$

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		pm2.04	$$⊢\left(\theta \to \left(\tau \to \eta \right)\right)\to \left(\tau \to \left(\theta \to \eta \right)\right)$$
3	1 2	syl8	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\tau \to \left(\theta \to \eta \right)\right)\right)\right)$$