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chain of equivalences

A step-by-step rewrite of a sentence, each step justified by a named law.

A chain of equivalences transforms one sentence into another through a sequence of sentences, each obtained from the previous one by replacing a part with something equivalent to it and naming the law used. Every sentence in the chain is equivalent to the first.

Examples

  • ¬(P → Q) ≡ ¬(¬P ∨ Q) (material implication) ≡ ¬¬P ∧ ¬Q (De Morgan) ≡ P ∧ ¬Q (double negation).

See also

replacement of equivalents logical equivalence
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