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Full Idea
The syntactic turnstile |- φ means 'There is a proof of φ' (in the system currently being considered). Another way of saying the same thing is 'φ is a theorem'.
Gist of Idea
The syntactic turnstile |- φ means 'there is a proof of φ' or 'φ is a theorem'
Source
David Bostock (Intermediate Logic [1997], 5.1)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.192
Related Ideas
Idea 13348 It seems more natural to express |= as 'therefore', rather than 'entails' [Bostock]
Idea 13349 Γ|=φ is 'entails'; Γ|= is 'is inconsistent'; |=φ is 'valid' [Bostock]