Functional Hausdorffness is hereditary

This article gives the statement, and possibly proof, of a topological space property (i.e., functionally Hausdorff space) satisfying a topological space metaproperty (i.e., subspace-hereditary property of topological spaces)
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Statement

Any subset of a functionally Hausdorff space, endowed with the subspace topology, is also a functionally Hausdorff space.