No, you use intuition to come up with an idea the use that idea to write a proof for yourself. Intuition is invaluable as a starting point, but it's often misleading.
https://terrytao.wordpress.com/career-advice/there%E2%80%99s...
> The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition.
In mathematics, intuition is the starting point and guiding principle, but never worth anything by itself without rigour.