(Solved): 9 Modus ponens is a rule of implication, which means that its conclusion can be inferred from its pr ...

Modus ponens is a rule of implication, which means that its conclusion can be inferred from its premises but may not be logically equivalent to those premises. All rules of implication can be applied only to the main operator of the statements matching the form of the rule. Monens states that if you have a conditional \( p \leq q \) on its own line, and if you have the antecedent \( p \) of that conditional on another line, then you can infer the consequent q on a new line. You can apply the modus ponens rule only if the conditional premise is on its own line with the horseshoe as the main operator. In other words, you cannot apply modus ponens to a part of a line. Remember that \( \rho \) and \( q \) can stand for any statement and that they may stand for compound statements with other operators (even other horseshoes) within. It does not matter whether the conditional statement is listed on a line before or after the line listing the conditional's antecedent. It only matters that you have two previous proof lines that match the form of the two statements in \( 1 . \) 2. \( R \vee \sim L \) 3. \( (D * R) \ni \sim(L \vee \sim B) \quad / \sim(L \vee \sim B) \) 4. \( \sim(L \vee \sim B) \quad 1,3 \mathrm{MP} \)