The predicate calculus has a number of theorems and axioms for proving logical statements. Here are the main symbols used in predicate calculus:

P(x) – proposition – a logical statement in the condition x.

x – any condition in the set of possible conditions.

c – a particular condition in the set of possible conditions.

" – "For every"

$ – "Exists"

® – Implication

Ù – Conjunction (logical and)

Ú – Disjunction (logical or)