Theorem 3anidm23

Description: Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007)

	Ref	Expression
Hypothesis	3anidm23.1	$$⊢\left(\phi \wedge \psi \wedge \psi \right)\to \chi$$
Assertion	3anidm23	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		3anidm23.1	$$⊢\left(\phi \wedge \psi \wedge \psi \right)\to \chi$$
2	1	3expa	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \psi \right)\to \chi$$
3	2	anabss3	$$⊢\left(\phi \wedge \psi \right)\to \chi$$