I've been trained in applied mathematics, and I just started exploring pure mathematics (real analysis, to be exact). I'm already stuck at a very simple proof, and was wondering if anybody can help me out:(adsbygoogle = window.adsbygoogle || []).push({});

http://img392.imageshack.us/img392/8971/proofeg2.png [Broken]

I understand it for the most part. However, I do not understand why the statement highlighted in yellow implies the statement that is highlighted in red. I copied that proof directly from Maxwell Rossenlicht's Introduction to Analysis.

Any help is greatly appreciated.

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# Help with simple proof - comlement of unions.

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