Independence Theorem The rules of inference and axiom schemata of f are independent Proof sketch Step 1 MP is independent Step 2 Gen is independent Step 3 Asl, AS2 and A S3 are independent Step 4 A 4 IS Independent etneⅤas Step 5 ASs is independent Do a transformation In a proof from hypothesis ab rule is independent Logic in Computer Science -p 4/19Independence Theorem The rules of inference and axiom schemata of F are independent. Proof Sketch: Step 1 MP is independent. Step 2 Gen is independent. Step 3 AS1, AS2 and AS3 are independent. Step 4 AS4 is independent. “Define”∀ as ∃. Step 5 AS5 is independent. Do a transformation. In a proof from hypothesis, αβ rule is independent. Logic in Computer Science – p.4/19