Any sentence provable from the empty set of premisses according to some syntactic consequence relation ${⊢}_{\text{L}}$ providing a proof theory for a logic $\text{L}$, i.e., an formula $\phi$ is an $\text{L}$-theorem when $\varnothing {⊢}_{\text{L}}\phi$ (or, more simply, ${⊢}_{\text{L}}\phi$). The semantic notion analogous to theoremhood of a formula $\phi$ is validity of $\phi$, i.e., that $\phi$ is true (or, more generally, assigned a designated value) in every model.