Theorem 3anidm12

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

	Ref	Expression
Hypothesis	3anidm12.1	$$⊢\left(\phi \wedge \phi \wedge \psi \right)\to \chi$$
Assertion	3anidm12	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		3anidm12.1	$$⊢\left(\phi \wedge \phi \wedge \psi \right)\to \chi$$
2	1	3expib	$$⊢\phi \to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
3	2	anabsi5	$$⊢\left(\phi \wedge \psi \right)\to \chi$$