Full Idea
If we write Γ |= φ, with one formula to the right, then the turnstile abbreviates 'entails'. For a sequent of the form Γ |= it can be read as 'is inconsistent'. For |= φ we read it as 'valid'.
Gist of Idea
Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid'
Source
David Bostock (Intermediate Logic [1997], 1.3)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.13
Related Idea
Idea 13623 The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem' [Bostock]