Theorem com23

Description: Commutation of antecedents. Swap 2nd and 3rd. Deduction associated with com12 . (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 4-Aug-2012)

	Ref	Expression
Hypothesis	com3.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	com23	$$⊢\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		com3.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		pm2.27	$$⊢\chi \to \left(\left(\chi \to \theta \right)\to \theta \right)$$
3	1 2	syl9	$$⊢\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)$$