Theorem anabs7

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996) (Proof shortened by Wolf Lammen, 17-Nov-2013)

	Ref	Expression
Assertion	anabs7	$$⊢\left(\psi \wedge \left(\phi \wedge \psi \right)\right)\leftrightarrow \left(\phi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		simpr	$$⊢\left(\phi \wedge \psi \right)\to \psi$$
2	1	pm4.71ri	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \left(\psi \wedge \left(\phi \wedge \psi \right)\right)$$
3	2	bicomi	$$⊢\left(\psi \wedge \left(\phi \wedge \psi \right)\right)\leftrightarrow \left(\phi \wedge \psi \right)$$