total order is explained as a binary relation with operator ≤ .
Using that definition with the following relationship a ≤ b ≤ c (1)
a ≤ a since a = a (reflexivity)
a ≤ b by (1)
a ≤ c by (1) (transivity)
b ≤ a if and only if b = a which also satisfies (1) (antisymmetry)
b ≤ b since b = b (reflexivity)
b ≤ c by (1)
c ≤ a if and only if c = a which also satisfies (1) (antisymmetry)(transivity)
c ≤ b if and only if c = b which also satisfies (1) (antisymmetry)
c ≤ c since c = c (reflexivity)
All these 2-tuple relations are true for binary relationship ≤, with assumed ordering relation (1).
If you intend something else, please explain your notation.