Can You Quote me a Mathematical Proof that Uses a Logic Formula other than Syllogism?

May 15, 2023
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There exist many other formulas of mathematical logic in "Principia Mathematica". Is there an example of a mathematical proof that uses one of them (not syllogism)?
Are you speaking about Isaac Newton's "Principia" that expounds Newton's laws of motion and his law of universal gravitation?

Or are you discussing "Principia" the three-volume work on the foundations of mathematics written by mathematician-philosophers Alfred North Whitehead and Bertrand Russell, published in 1910, 1912, and 1913?

It is critical to adequately identify which work you suggest that our investigations involve.

However, I suspect you mean Whitehead's and Russell's work because it contains a derivation of large portions of mathematics using both notions and principles of symbolic logic.