What a Proof Is · Hard problem

If $x^2 - 5x + 6 = 0$ and $x > 0$, then $x = 3$

If $x^2 - 5x + 6 = 0$ and $x$ is odd, then $x = 3$

If $x^2 - 5x + 6 = 0$ and $x$ is prime, then $x = 3$

If $x^2 - 5x + 6 = 0$, then $x = 2$