---
tag: 4N2HHE7PC1
kind: concept
name: Tautological consequence
sources:
  - wikipedia: en:34235295@r1310222722
    locator: Tautological consequence
    note: adopted
    mention: wikipedia://en/34235295
    sections: [Summary]
same_as:
  wikidata: Q7688961
  wikipedia: Tautological consequence
inventory: [V4V08TW68N]
---

## Summary

In [[propositional logic|09K9MWD2QQ]], **tautological consequence** is a strict form of logical consequence in which the [[tautologousness|05006AJ7DZ]] of a [[proposition|0ZGC7ZESYN]] is preserved from one line of a proof to the next. Not all logical consequences are tautological consequences. A [[proposition|0ZGC7ZESYN]] $Q$ is said to be a tautological consequence of one or more other propositions ($P_1$, $P_2$, ..., $P_n$) in a proof with respect to some logical system if one is validly able to introduce the proposition onto a line of the proof within the rules of the system; and in all cases when each of ($P_1$, $P_2$, ..., $P_n$) are true, the proposition $Q$ also is true.