What is wrong with this proof that 3 is less than 1?

What is wrong with this proof?
Theorem. 3 is less than 1.
Proof. Every number is either less than 1 or greater than 1
or equals 1. Let $c$ be an arbitrary number. Therefore, it is less

than 1 or greater than 1 or equals 1. Suppose it is less than 1. By the
rule of universal generalization, if an arbitrary number is less than 1,
every number is less than 1. Therefore, 3 is less than 1.