Full Idea
If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'.
Gist of Idea
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises
Source
JC Beall / G Restall (Logical Consequence [2005], 4)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.8
A Reaction
These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules.