# Logical Biconditional - Rules of Inference

Rules of Inference

Like all connectives in first-order logic, the biconditional has rules of inference that govern its use in formal proofs.

### Other articles related to "rules of inference, rules":

Logical Biconditional - Rules of Inference - Biconditional Elimination
... 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 ... Formally ( A ↔ B ) ∴ ( A → B ) also ( A ↔ B ) ∴ ( B → A ) ...
Existential Quantification - Properties - Rules of Inference
... Transformation rules Propositional calculus Rules of inference Modus ponens Modus tollens Biconditional introduction Biconditional elimination Conjunction introduction Simplification Disjunction ... There are several rules of inference which utilize the existential quantifier ...

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The great challenge which faces us is to assure that, in our society of big-ness, we do not strangle the voice of creativity, that the rules of the game do not come to overshadow its purpose, that the grand orchestration of society leaves ample room for the man who marches to the music of another drummer.
Hubert H. Humphrey (1911–1978)

I have heard that whoever loves is in no condition old. I have heard that whenever the name of man is spoken, the doctrine of immortality is announced; it cleaves to his constitution. The mode of it baffles our wit, and no whisper comes to us from the other side. But the inference from the working of intellect, hiving knowledge, hiving skill,—at the end of life just ready to be born,—affirms the inspirations of affection and of the moral sentiment.
Ralph Waldo Emerson (1803–1882)

Alas! when Virtue sits high aloft on a frigate’s poop, when Virtue is crowned in the cabin of a Commodore, when Virtue rules by compulsion, and domineers over Vice as a slave, then Virtue, though her mandates be outwardly observed, bears little interior sway.
Herman Melville (1819–1891)