Full Idea
In classical logic, Monotony follows immediately from the nature of the relation |=, for Γ |= φ holds precisely when φ is true on every interpretation on which all sentences in Γ are true.
Gist of Idea
In classical logic the relation |= has Monotony built into its definition
Source
G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
That is, semantic consequence (|=) is defined in terms of a sentence (φ) always being true if some other bunch of sentences (Γ) are true. Hence the addition of further sentences to Γ will make no difference - which is Monotony.