What does the symbol :: mean in math

f (S)::={b ∈ B | f(s) = b for some s ∈ S}
what does the symbol :: mean in this equation?

please be specific
TIA

I've only ever seen the double colon used in proportions to mean "as," i.e. a:b :: b:c. I think the symbol in question is :=, the colon-equals. It means "is defined as."