Consistency is preserved under unions of chains because proofs use finitely many assumptions. A maximal consistent extension then gives a valuation through its truth lemma, proving propositional completeness.

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  1. Maximal consistent set truth lemma
  2. Completeness theorem for propositional logic
  3. Propositional logic
  4. Mathematical logic
  5. Foundations of mathematics
  6. Area of mathematics
  7. Mathematics
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