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Full Idea
An axiomatic system is most naturally consistent iff no thesis is the negation of another thesis. It can be shown that every axiom is valid, that the transformation rules are validity-preserving, and if a wff α is valid, then ¬α is not valid.
Gist of Idea
The rules preserve validity from the axioms, so no thesis negates any other thesis
Source
GE Hughes/M Cresswell (An Introduction to Modal Logic [1968], Ch.1)
Book Ref
Hughes,G./Cresswell,M.: 'An Introduction to Modal Logic' [Methuen 1972], p.19
A Reaction
[The labels 'soundness' and 'consistency' seem interchangeable here, with the former nowadays preferred]