Contrapositive with primes

Contrapositive. "If $p$ is prime and $p>2$, then $p$ is odd" is equivalent to "if $p$ is even (and prime), then $p\le2$".

Proof. If $p$ is even prime, $p=2k$ for some $k$. Since $p$ is prime and $2\mid p$, either $p=2$ (so $k=1$) or $p$ is composite. Primality forces $p=2$.

Conclusion. All primes $p>2$ are odd.