Theorem anasss

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by NM, 15-Nov-2002)

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

Proof

Step	Hyp	Ref	Expression
1		anasss.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	imp32	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$