Four equality relation axioms - iaminfinityiq/successor-function GitHub Wiki

The next four following axioms are equality relation axioms, which includes:

For every x, x = x. Equality is reflective
For every x, y that satisfies x = y, then y = x. Equality is symmetric
For every x, y, z that satisfies x = y and y = z, then x = z. Equality is transitive
For all a and b, if a is a natural number then so does b. The natural numbers are closed within equality