Replacing a designated subformula by a logically equivalent formula preserves logical equivalence of the surrounding propositional formulas. For any Boolean valuation the two expressions at the replaced node have the same truth value. Each logical connective preserves this agreement when its other inputs are unchanged. Induction from that node to the root proves agreement of the whole formulas under every valuation.

Ancestors (9)

  1. Subformula replacement theorem
  2. Subformula
  3. Propositional formula
  4. Propositional logic
  5. Mathematical logic
  6. Foundations of mathematics
  7. Area of mathematics
  8. Mathematics
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