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replacement of equivalents

Swapping a part of a sentence for something equivalent keeps the whole equivalent.

If B ≡ C, then replacing an occurrence of B inside a sentence A with C produces a sentence equivalent to A. This is what licenses each step of a chain of equivalences.

Examples

  • Since ¬¬Q ≡ Q, the sentence P ∧ ¬¬Q is equivalent to P ∧ Q.

See also

chain of equivalences
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