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Let $M$ be a finite extension of $E$ and let $E$ be a finite extension of $F$. Then $M$ is a finite extension of $F$ and $[M:F] = [M:E][E:F]$.

Is there an easy explanation and/or proof for this theorem? My instructor gave an incomplete proof in class but got stuck and I'm kind of confused of what's going on.

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    I would be surprised if you could pick a textbook on field theory which does not prove this in detail!2011-11-23

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