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Theorem 3anidm 1098
Description: Idempotent law for conjunction. (Contributed by Peter Mazsa, 17-Oct-2023.)
Assertion
Ref Expression
3anidm ((𝜑𝜑𝜑) ↔ 𝜑)

Proof of Theorem 3anidm
StepHypRef Expression
1 df-3an 1083 . 2 ((𝜑𝜑𝜑) ↔ ((𝜑𝜑) ∧ 𝜑))
2 anabs1 658 . 2 (((𝜑𝜑) ∧ 𝜑) ↔ (𝜑𝜑))
3 anidm 565 . 2 ((𝜑𝜑) ↔ 𝜑)
41, 2, 33bitri 298 1 ((𝜑𝜑𝜑) ↔ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  w3a 1081
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 208  df-an 397  df-3an 1083
This theorem is referenced by:  relcnvtr  6117
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