Theorem anabss7

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 19-Nov-2013)

	Ref	Expression
Hypothesis	anabss7.1	$$⊢\left(\psi \wedge \left(\phi \wedge \psi \right)\right)\to \chi$$
Assertion	anabss7	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		anabss7.1	$$⊢\left(\psi \wedge \left(\phi \wedge \psi \right)\right)\to \chi$$
2	1	anassrs	$$⊢\left(\left(\psi \wedge \phi \right)\wedge \psi \right)\to \chi$$
3	2	anabss4	$$⊢\left(\phi \wedge \psi \right)\to \chi$$