Full Idea
In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!).
Gist of Idea
Since first-order languages are complete, |= and |- have the same meaning
Source
Wilfrid Hodges (Model Theory [2005], 3)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.8
A Reaction
[actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy!