Theorem anabsi7

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 18-Nov-2013)

	Ref	Expression
Hypothesis	anabsi7.1	$$⊢\psi \to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
Assertion	anabsi7	$$⊢\left(\phi \wedge \psi \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		anabsi7.1	$$⊢\psi \to \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
2	1	anabsi6	$$⊢\left(\psi \wedge \phi \right)\to \chi$$
3	2	ancoms	$$⊢\left(\phi \wedge \psi \right)\to \chi$$