Theorem anidmdbi

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

	Ref	Expression
Assertion	anidmdbi	⊢ ( ( 𝜑 → ( 𝜓 ∧ 𝜓 ) ) ↔ ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		anidm	⊢ ( ( 𝜓 ∧ 𝜓 ) ↔ 𝜓 )
2	1	imbi2i	⊢ ( ( 𝜑 → ( 𝜓 ∧ 𝜓 ) ) ↔ ( 𝜑 → 𝜓 ) )