Independence of p The axiom schemata and the rule of inference of p are all independent Proof sketch It is trivial to see that mp is independent. For the rest, using Arithmetic Interpretation It suffices to find some property which the axiom does not have but which all the other axioms of the sys tem do have and which is preserved by the rules of terence Logic in Computer Science-p 13/17Independence of P The axiom schemata and the rule of inference of P are all independent. Proof Sketch: It is trivial to see that MP is independent. For the rest, using Arithmetic Interpretation. It suffices to find some property which the axiom does not have but which all the other axioms of the sys￾tem do have, and which is preserved by the rules of inference. Logic in Computer Science – p.13/17