Theorem anidmdbi

Description: Conjunction idempotence with antecedent. (Contributed by Roy F. Longton, 8-Aug-2005)

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

Proof

Step	Hyp	Ref	Expression
1		anidm	$$⊢\left(\psi \wedge \psi \right)\leftrightarrow \psi$$
2	1	imbi2i	$$⊢\left(\phi \to \left(\psi \wedge \psi \right)\right)\leftrightarrow \left(\phi \to \psi \right)$$