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We prove the result in the title. We infer, that unlike cylindric algebras,there is a first order axiomatization of the class of completely representablepolyadic algebras of infinite dimension, though the one we obtain is infinite;in fact uncountable, but shares a single schema, stipulating that the(uncountably many)substitution operators are completely additive. Similarresults are obtained for non commutative reducts of polyadic equality algebrasof infinite dimensions, where we can drop complete additivity. However, itremains unknown to us whether there are atomic polyadic algebras of infinitedimension that are not completely additive; but we strongly conjecture thatthere are.

A polyadic algebra of infinite dimension is completely representable if and only if it is atomic and completely additive