Material Implication (rule of Inference)

Material Implication (rule Of Inference)

For other uses of the term see Material implication (disambiguation).

Transformation rules
Propositional calculus

Rules of inference
Modus ponens
Modus tollens
Biconditional introduction
Biconditional elimination
Conjunction introduction
Simplification
Disjunction introduction
Disjunction elimination
Disjunctive syllogism
Hypothetical syllogism
Constructive dilemma
Destructive dilemma
Absorption

Rules of replacement

Associativity
Commutativity
Distributivity
Double negation
De Morgan's laws
Transposition
Material implication
Exportation
Tautology
Predicate logic
Universal generalization
Universal instantiation
Existential generalization
Existential instantiation

In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction if and only if the antecedent is negated. The rule states that P implies Q is logically equivalent to not-P or Q and can replace each other in logical proofs.

Where "" is a metalogical symbol representing "can be replaced in a proof with."

Read more about Material Implication (rule Of Inference):  Formal Notation, Example

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