Theorem an13s

Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006)

	Ref	Expression
Hypothesis	an12s.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
Assertion	an13s	$$⊢\left(\chi \wedge \left(\psi \wedge \phi \right)\right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		an12s.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
2	1	exp32	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	com13	$$⊢\chi \to \left(\psi \to \left(\phi \to \theta \right)\right)$$
4	3	imp32	$$⊢\left(\chi \wedge \left(\psi \wedge \phi \right)\right)\to \theta$$