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Metamath Proof Explorer

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 ) )