Identity Elimination

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It looks like this:

What does it mean?

It means that if you have both a sentence, P(n), containing a constant, n, and an identity sentence, n=m, containing constants n and m, then you may insert any sentence that results from replacing any occurrences of n, in P(n) with occurrences of m.

So, for example, if you had R(a, c) and a=b, you could insert R(b, c).

In addition, if you had R(a, a),  and a=b, you could write any of the following: R(b, b), R(a, b), and R(b, a).

 

Coming soon to a logic class near you!