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FUNCTIONAL CALCULI OF FIRST ORDER
THE PURE FUNCTIONAL CALCULUS OF FIRST
FUNCTIONAL CALCULI OF HIGHER ORDER
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abbreviation axiom of choice axiom of infinity axioms and rules axioms of extensionality axioms of F axioms of well-ordering Bernays brackets Corollary decision problem deduction theorem definition disjunction domain of individuals dual equivalent existential quantifier f 3 f f t f finite number follows formulas in prenex free individual variables free occurrences free variables func function of individuals Functional Calculi functional constant functional variables appearing given formula Hence individual constant lemma logistic system Math modus ponens natural numbers negation non-empty domain notation obtained preceding prefix prenex normal form primitive symbols Proof propositional and functional Propositional Calculus propositional functions propositional variables proved Pure Functional Calculus quantifier-free real number replacing result rule of substitution rules of inference set of values singulary Skolem normal form statement syntactic theorems syntax language tautology theorem of F theory of types tion tional variable truth-tables universal quantifier VIII Zermelo