  A metric algebra is a metric variant of the notion of $\Sigma$-algebra, first
introduced in universal algebra to deal with algebras equipped with metric
structures such as normed vector spaces. In this paper, we showed metric
versions of the variety theorem, which characterizes strict varieties (classes
of metric algebras defined by metric equations) and continuous varieties
(classes defined by a continuous family of basic quantitative inferences) by
means of closure properties. To this aim, we introduce the notion of
congruential pseudometric on a metric algebra, which corresponds to congruence
in classical universal algebra, and we investigate its structure.
