Full Idea
I introduce the sign |- to mean 'we may validly conclude'. To call it the 'assertion sign' is misleading. It may conveniently be read as 'therefore'.
Gist of Idea
The sign |- may be read as 'therefore'
Source
E.J. Lemmon (Beginning Logic [1965], 1.2)
Book Reference
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.11
A Reaction
[Actually no gap between the vertical and horizontal strokes of the sign] As well as meaning 'assertion', it may also mean 'it is a theorem that' (with no proof shown).