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4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL

[any formula which has a proof is a valid formula]

2 ideas
If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon]
The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell]