I have recently learned what are valid expressions in first order logic. Now I wonder what are "derivation rules" of first order logic. By a "derivation rule" I mean a rule that can take a first order logic expression and "generate" another expression that follow from it. Or, in a more general case, it take two expressions formulated with FOL syntax and generate a new (third) expression that follow from the original two expressions.
I guess that should be a known, well established list of those rules but for whatever reason I cannot find it. Can it be the case that I have some misconception?