Material Implication (rule of Inference) - Formal Notation

Formal Notation

The material implication rule may be written in sequent notation:

where is a metalogical symbol meaning that is a syntactic consequence of in some logical system;

or in rule form:

where the rule is that wherever an instance of "" appears on a line of a proof, it can be replaced with "";

or as the statement of a truth-functional tautology or theorem of propositional logic:

where and are propositions expressed in some formal system.