Theorem 3anassrs

Description: Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017)

	Ref	Expression
Hypothesis	3anassrs.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \tau$$
Assertion	3anassrs	$$⊢\left(\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\wedge \theta \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		3anassrs.1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \tau$$
2	1	3exp2	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$
3	2	imp41	$$⊢\left(\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\wedge \theta \right)\to \tau$$