Theorem com34

Description: Commutation of antecedents. Swap 3rd and 4th. Deduction associated with com23 . Double deduction associated with com12 . (Contributed by NM, 25-Apr-1994)

	Ref	Expression
Hypothesis	com4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
Assertion	com34	$$⊢\phi \to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		com4.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
2		pm2.04	$$⊢\left(\chi \to \left(\theta \to \tau \right)\right)\to \left(\theta \to \left(\chi \to \tau \right)\right)$$
3	1 2	syl6	$$⊢\phi \to \left(\psi \to \left(\theta \to \left(\chi \to \tau \right)\right)\right)$$