  In other words, a proposition is necessary (or expresses a necessary truth) if, in analyzing it, one arrives at a statement of identities. A simple example can be found in arithmetic: “2+2 = 4.” Since “2 = 1+1” and “4 = 1+1+1+1”, we can easily show that the original statement can be reduced to “1+1+1+1 = 1+1+1+1.” Here we have an obvious case of an identity and one where we can say that the concept of the predicate – in this case, “4” – is contained is contained in the subject, “2+2” (or “(1+1) + (1+1)”).