The author frequently refers to Principia Mathematica by Alfred North Whitehead and Bertrand Russell. The major contribution of Principia Mathematica is its notation and rules of inference, which can be grasped with a little effort. Even if the reader has only had high-school Geometry or Algerbra II, if persistant he or she should be able to make sense of the logical formulas in the proof. A when used in a formula represents the truth-value of the statement behind A . A statement may be determined true or false by observation - or it may also by deduced from an initial set of axioms within a system.
Theorems are simply statments deduced from the initial axioms, or any theorems already proven.
And finally, the author sometimes uses the operators and interchangeably. The actual proof is quite 'typographically complex' and I have formatted this document to utilize the Symbol Truetype font for the logical symbols needed to convey its meaning adequately. If the above logical statements are readable in your browser, then the proof will be also. I have made a tremendous effort to preserve the original look of the text in HTML format. Every reference in the texts has been replaced with a hyperlink to the appropriate location in the proof, if possible.