Is this proof by counterexample valid?

Question

This is the given statement and its proof:

$$\exists m \in Z^+, \forall n \in Z^+, m<n$$

Proof: This result is false because, for each positive integer m, if we put $n=m$ then n is a positive integer and $m \nless n$.

If I say:

"This statement is false and a counterexample is $n=1$ since $m \nless 1$ for all positive integers m."

would it be a valid alternative proof?

Answer 1

Yes. You can disprove any statement by showing that the statement has a counterexample.