Biconditional Elimination

Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional. If is true, then one may infer that is true, and also that is true. For example, if it's true that I'm breathing if and only if I'm alive, then it's true that if I'm breathing, I'm alive; likewise, it's true that if I'm alive, I'm breathing. The rules can be stated formally as:


where the rule is that wherever an instance of "" appears on a line of a proof, either "" or "" can be placed on a subsequent line;

Read more about Biconditional Elimination:  Formal Notation

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Biconditional Elimination - Formal Notation
... The biconditional elimination rule may be written in sequent notation and where is a metalogical symbol meaning that, in the first case, and in the other are syntactic consequences of in some logical ...
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... Biconditional elimination allows one to infer a conditional from a biconditional if ( A B ) is true, then one may infer one direction of the biconditional, ( A B ...

Famous quotes containing the word elimination:

    To reduce the imagination to a state of slavery—even though it would mean the elimination of what is commonly called happiness—is to betray all sense of absolute justice within oneself. Imagination alone offers me some intimation of what can be.
    André Breton (1896–1966)