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Full Idea
In predicate calculus we take over the propositional connectives and propositional variables - but we need additional rules for handling quantifiers: four rules, an introduction and elimination rule for the universal and existential quantifiers.
Gist of Idea
Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules
Source
E.J. Lemmon (Beginning Logic [1965])
Book Ref
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.104
A Reaction
This is Lemmon's natural deduction approach (invented by Gentzen), which is largely built on introduction and elimination rules.