Theorem anabsan

Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996)

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

Proof

Step	Hyp	Ref	Expression
1		anabsan.1	$$⊢\left(\left(\phi \wedge \phi \right)\wedge \psi \right)\to \chi$$
2		pm4.24	$$⊢\phi \leftrightarrow \left(\phi \wedge \phi \right)$$
3	2 1	sylanb	$$⊢\left(\phi \wedge \psi \right)\to \chi$$