See also contraposition and proof by contrapositive. A proof by contraposition (contrapositive) is a direct proof of the contrapositive of a statement. Modus tollens (also known as "the law of contrapositive") is a deductive rule of inference. One can also prove a theorem by proving the contrapositive of the theorem's statement. Finally, since differentiability implies continuity, the contrapositive states "discontinuity" implies non-differentiability. This is often called the "law of contrapositive", or the "modus tollens" rule of inference. The previous example employed the contrapositive of a definition to prove a theorem. This function is monotonic, so we have the zero-one principle as the contrapositive. This mode of argument is the contrapositive of proof by complete induction. We use the contrapositive of the definition of injectivity, namely that if , then . Having proved the contrapositive, we can then infer that the original statement is true. However, via the contrapositive, it's true that formula 31 implies formula 32. In traditional logic there is more than one contrapositive inferred from each original statement. The contrapositive of this statement is also true. This contrapositive, like the original statement, is also true.