**Modis Ponens**, also known as **Conditional Elimination** and **Modus ponendo ponens** ^{[1]}^{[2]}, is a rule of inference in propositional logic that states that if we have a material condtional that has a true antecedent, then we may infer the consequent of the antedent. In other words, if P implies Q is true and P is true, then we may infer that Q is true. This is often stated symbolically in rule form as:

In sequent notation, it could be expressed as:

As a theorem of propositional logic, it is expressed as:

In all three expressions above, and are metasyntactic variables representing well-formed formulas of propositional logic.

## ReferencesEdit

- ↑ Ikenaga, B. "Rules of Inference and Logic Proofs". Retrieved from http://sites.millersville.edu/bikenaga/math-proof/rules-of-inference/rules-of-inference.htmlhttp://sites.millersville.edu/bikenaga/math-proof/rules-of-inference/rules-of-inference.html.
- ↑ Margaris, A. (1967).
*First Order Mathematical Logic*. Blaisdell Publishing Company.

**Rules of inference**

**Modus Ponens** | Modus Tollens | Disjunctive Syllogism | Hypothetical Syllogism | Conjunction Introduction | Conjunction Elimination | Disjunction Introduction | Disjunction Elimination | Bicondional Introduction | Biconditional Elimination | Constructive Dilemma | Destructive Dilemma | Absorption | Modus ponendo tollens

**Rules of Transformation**

Double Negation | Associative property | Commutative property | Distributive property | DeMorgan's Laws | Tautology | Exportation | Material Implication | Transposition