Theorem anabss3

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 1-Jan-2013)

	Ref	Expression
Hypothesis	anabss3.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \psi \right)\to \chi$$
Assertion	anabss3	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		anabss3.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \psi \right)\to \chi$$
2	1	anasss	$$⊢\left(\phi \wedge \left(\psi \wedge \psi \right)\right)\to \chi$$
3	2	anabsan2	$$⊢\left(\phi \wedge \psi \right)\to \chi$$