The equality introduction rule is reflexivity, with no premise. The equality elimination rule is substitution of equal first-order terms into a first-order formula:
(1)
The indicated substitution must be capture-avoiding substitution in first-order logic: the first-order terms must be free for the replaced variable. One can designate a particular argument occurrence by choosing appropriately; the rule does not demand replacing every occurrence of an identical-looking term in a formula.

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