How do you know if a relation is antisymmetric

For example relation IR on N such that " n1 R n2 " iff "n1 >=n2" for all n1,n2 € N

I think it's antisymmetric but I don't know how to prove it

Antisymmetry means aRb & bRa ⇒ a = b

So here we have a ≤ b and b ≤ a If we combine these then we have
b ≤ a ≤ b

which essentially says that a is being squeezed between the same number so it must be b itself. Therefore a = b.