Here the antecedent or underlying supposition is the existence of a genuine counterpart. The necessary consequence is what would follow if that supposition were true. If the necessary consequence is denied, the supposition cannot be maintained under that implication.
The reasoning has the form: “If the first claim were true, the second result would follow; the second result is denied; therefore the first claim fails.” This attends to the relation of implication rather than merely noticing that the word “like” occurs twice.
The pattern cannot be applied between arbitrarily associated statements: the stated consequence must actually follow from the supposition.