 Russell  took up Frege's logic, but used the notation and formal rules of proof of Peano, in a paper of 1906 with the title “The theory of implication.”  Its formal machinery is exactly the same as Peano's. In later work, Russell changed the axiomatic system and the one of Principia Mathematica (Whitehead and Russell 1910–13) became standard. Russell's philosophical idea, and here he followed Frege, was that the axioms express basic logical truths, and other logical truths are derived from these through modus ponens and universal generalization, the two principles Frege had identified. Mathematics was to be reduced to logic, so that its proofs would become presented in the same axiomatic pattern.