The discussion centers on proving the expression (x = y) leading to the equivalence [(y = x) <--> (y = y)] using axioms from the theory of equality. It is established that no axioms are necessary for the truth of the formula in the standard interpretation of natural numbers, as any closed formula is inherently true or false. For derivability, the application of Leibniz's law is crucial for the left-to-right direction, while reflexivity is essential for the right-to-left direction.
PREREQUISITESMathematicians, logicians, and students of formal logic seeking to deepen their understanding of proof techniques and the foundations of equality in arithmetic.