**Teaching page of Shervine Amidi, Graduate Student at Stanford University. **

**This elimination rule is sometimes called “ modus ponens”. **

**Modus** **Ponens** or Law of Detachment Example: Let p be “It is snowing. .

**Biconditional introduction (↔ Intro) P Q Q P P ↔ Q This rule is, effectively, a double use of → Intro. **

**Thus, Modus Ponens has the form of a valid argument. **

**. . P is true. **

**q 1, 2, modus ponens 4. **

**. P is true. In this case, we have written ( modus ponens). **

**It can be summarized as "P implies Q. Thus, we say, for the above example, that the third line is derived from the earlier two lines using modus ponens. **

**In simboli la scriviamo cos X;X ! Y Y In questi episodio chiamer o S 0 il sistema assiomatico costituito dagli assiomi in A 1 e A 2 e dalla regola di inferenza Modus Ponens. **

**” “Therefore , I will study discrete math. **

**• If is a theorem (provable), –We can prove or. . **

**If antecedent = true, consequence = true. . **

**P is true.****P is true. **

**We already proved that modus ponens is sound, and now we have that it is complete (for Horn clauses). **

**. Therefore Q must also be true. , modus ponens) with the children as premises. **

**. s 3, 4, modus ponens 6. Notice that with one exception, the laws are paired in such a way that exchanging the symbols ∧, ∨, 1 and 0 for ∨, ∧, 0, and 1, respectively, in any law gives you a second law. ” “Therefore , I will study discrete math. . **

**. **

**Definition 2. On the right-hand side of a rule, we often write the name of the rule. **

**In propositional logic, modus ponens ( / ˈmoʊdəs ˈpoʊnɛnz /; MP ), also known as modus ponendo ponens ( Latin for "method of putting by placing"), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. **

**Similarly, if A→S is outside the scope of H, apply axiom 1, (A→S)→(H→(A→S)), and modus ponens to get H→(A→S). **

**p →s 1, 5, direct method of proof MSU/CSE 260 Fall 2009 15 Example: Contrapositive proof Prove hypothetical syllogism. **

**P is true. **

**. **