\vDashThe symbol \vDash is used in logic to denote semantic entailment or syntactic consequence. It indicates that a set of formulas logically entails another formula, meaning that if the premises are true, the conclusion must also be true.
A semantically entails B, meaning if A is true, B must also be true.
A \vDash BThe set of sentences \Gamma semantically entails the sentence \phi.
\Gamma \vDash \phiThe set of axioms \Sigma entails the proposition \psi.
\Sigma \vDash \psi