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Martin Sleziak
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Taras Banakh
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Every linear topological space embeds into the Tychonoff product of linear metric spaces

I need a reference to the following (known?)

Fact. Every topological vector space $X$ over the field of real numbers is topologically isomorphic to a linear subspace of the Tychonoff product of linear metric spaces.

This seems to be a basic fact in the theory of topological vector spaces, but I did not find it in the classical textbooks: Bourbaki, Schaefer, Rolewicz, Robertson&Robertson. If you know a suitable reference, please help!