The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.
Consistency
See also
Axiomatic Set Theory, Axiomatic System, Complete Axiomatic Theory, Consistency Strength, Gödel's First Incompleteness Theorem, Gödel's Second Incompleteness TheoremExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Consistency." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Consistency.html