Built-in function to know if a list is inside another?

Question

For example, if the function is f[a_List,b_List] then in f[{a,b,c},{a,b}] and f[{a,b,c},{b,c}] should return true but false in f[{a,b,c},{c,b}] or f[{a,b,c},{a,c}].

Any built in functions that do this, or a fast workaround?

An ugly way to do it is

And@@Table[MemberQ[b,a[[i]]],{i,Length@a}]

but I'm looking for a better or built-in function.