Theorem anabss1

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 31-Dec-2012)

	Ref	Expression
Hypothesis	anabss1.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \phi \right)\to \chi$$
Assertion	anabss1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		anabss1.1	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \phi \right)\to \chi$$
2	1	an32s	$$⊢\left(\left(\phi \wedge \phi \right)\wedge \psi \right)\to \chi$$
3	2	anabsan	$$⊢\left(\phi \wedge \psi \right)\to \chi$$