Early Action to BOTH Yale and U. of Chicago?

Question: Hello, so I'm currently working on my application for Yale's Single Choice Early Action admissions deadline. In the terms it says that applicants may apply to another school's rolling admission, and I am wanting to apply to The University of Chicago's non-binding Early Action which is 'open'. My question is: can I apply to both Early Action programs, seeing as they're both non-binding?

Wishful thinking! You CANNOT apply to U. of Chicago via non-binding Early Action if you are applying to Yale via the Single-Choice Early Action option.

Yale spells out their Early Action rules pretty clearly on their Web site. They say:

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