... use in the rest of mathematics and in related fields In any case, mathematical logic is concerned with formalizing and analyzing the kinds of reasoning used in the rest of mathematics The point ... using the connectives and parentheses in particular ways For example, A1 123, (A2 → ( A0 )), and ((( A1 ) → (A1 → A7 )) → A7 ) are all formulas, but X3 , (A5 ), () A4 1, A5 → A7 , and (A2 → ( A0 ) are ... Replacing α, β, and γ by particular formulas of LP in any one of the schemas A1 , A2 , or A3 gives an axiom of LP For example, (A1 → (A4 → A1 )) is an axiom, being an instance of axiom schema A1 ,...