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We show that whenever $Q \\subset M$ is a von Neumann subalgebra with separable predual such that both $Q$ and $Q \\cap M_1$ are the ranges of faithful normal conditional expectations and such that both the intersection $Q \\cap M_1$ and the central sequence algebra $Q' \\cap M^\\omega$ are diffuse (e.g. $Q$ is amenable), then $Q$ must sit inside $M_1$. 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