Theorem 3anidm13

Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008)

	Ref	Expression
Hypothesis	3anidm13.1	$$⊢\left(\phi \wedge \psi \wedge \phi \right)\to \chi$$
Assertion	3anidm13	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		3anidm13.1	$$⊢\left(\phi \wedge \psi \wedge \phi \right)\to \chi$$
2	1	3com23	$$⊢\left(\phi \wedge \phi \wedge \psi \right)\to \chi$$
3	2	3anidm12	$$⊢\left(\phi \wedge \psi \right)\to \chi$$