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The step from propositional logic to predicate logic is taken by moving from just truth values to structures with elements. This makes it possible to handle important and realistic mathematical structure, e.g. groups, fields, …In order to discuss these structures one needs names (constants for elements) and variables. Furthermore one wants to extend and to for all: φ(a)∧varphi(b) to ∀xφ(x). Similarly for or and exists. Again suitable inductive procedures provide the reader with all the tools one needs. Defining truth values for the new kind of statements becomes a little bit more complicated. Gentzen’s Natural Deduction extends without problems to predicate logic, one has to keep track of one’s variables. Again the reader will have no problem to make his own derivations. Soundness—derivable ⇒ true—does not present any problem.