Theorem ancom1s

Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Hypothesis	an32s.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	ancom1s	$$⊢\left(\left(\psi \wedge \phi \right)\wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		an32s.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
2		pm3.22	$$⊢\left(\psi \wedge \phi \right)\to \left(\phi \wedge \psi \right)$$
3	2 1	sylan	$$⊢\left(\left(\psi \wedge \phi \right)\wedge \chi \right)\to \theta$$