# How can you translate the mathematical statement 5=5 into a second order symbolic logic statement?

Hi I'm trying to describe the statement 5=5 using symbolic logic. I initially attempted to describe this into English as:

There is such a thing x and such a thing y, such that x is equivalent to y, iif for all x, x equals {a,b,c,d,e} AND for all y, y equals {a,b,c,d,e}.

and then more formally as:

(x)(y)((x=y)≡(∀x(x={ a, b, c, d, e}) ∧ ∀y(y={ a, b, c, d, e}))

Is this correct? Does it even make sense?

• It follows directly from the axioms of set theory. – Atamiri Mar 28 '15 at 17:29

(5=5) is already an atomic sentence in FOL=. It evaluates to true. If you wanted, you could get unnecessarily complicated and say something like ∀x∀y(((x=5)∧(y=5))→(x=y)) but this idea is already incorporated into what = does.