Theorem com4l

Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994) (Proof shortened by Mel L. O'Cat, 15-Aug-2004)

	Ref	Expression
Hypothesis	com4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
Assertion	com4l	$$⊢\psi \to \left(\chi \to \left(\theta \to \left(\phi \to \tau \right)\right)\right)$$

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	com3l	$$⊢\psi \to \left(\chi \to \left(\phi \to \left(\theta \to \tau \right)\right)\right)$$
3	2	com34	$$⊢\psi \to \left(\chi \to \left(\theta \to \left(\phi \to \tau \right)\right)\right)$$