Is a Schauder Basis a minimal total set?

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Given that the span of Schauder Basis - $S\subset V$ is $V$ itself, this implies that it is a total set. My teacher said that it was minimal as well but did not go on to prove it. I suspect it might be true given the uniqueness of representations of vectors in the "span" of a Schauder basis but I can't seem to show it.