Theorem anabss5

Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994) (Proof shortened by Wolf Lammen, 1-Jan-2013)

	Ref	Expression
Hypothesis	anabss5.1	$$⊢\left(\phi \wedge \left(\phi \wedge \psi \right)\right)\to \chi$$
Assertion	anabss5	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		anabss5.1	$$⊢\left(\phi \wedge \left(\phi \wedge \psi \right)\right)\to \chi$$
2	1	anassrs	$$⊢\left(\left(\phi \wedge \phi \right)\wedge \psi \right)\to \chi$$
3	2	anabsan	$$⊢\left(\phi \wedge \psi \right)\to \chi$$