I think you and OP are talking about different things because the term "intuitionist" has been used for both the philosophy that EJ Brouwer espoused (which matches what OP said) and the large field of constructive mathematics that has been greatly influenced by Brouwer's philosophy but has embraced approaches like formal logic which Brouwer himself disliked.

I was merely pointing out that the "mental" dependency of intuitionism isn't strictly necessary. Take it out, and you're left with an equally valid constructive logic.