We offer an elementary theorem on ideals in the disc algebra
A
(
D
)
A({\mathbf {D}})
, which by way of a corollary, one, identifies the maximal ideals of
A
(
D
)
A({\mathbf {D}})
, and two, provides a proof, which avoids the axiom of choice, that every proper ideal in
A
(
D
)
A({\mathbf {D}})
is contained in a maximal ideal.