Theorem an31s

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

	Ref	Expression
Hypothesis	an32s.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	an31s	$$⊢\left(\left(\chi \wedge \psi \right)\wedge \phi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		an32s.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
2	1	exp31	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	com13	$$⊢\chi \to \left(\psi \to \left(\phi \to \theta \right)\right)$$
4	3	imp31	$$⊢\left(\left(\chi \wedge \psi \right)\wedge \phi \right)\to \theta$$