Full Idea
Although intuitionistic propositional and first-order logics are sub-systems of the corresponding classical systems, intuitionistic second-order logic affirms the negations of some classical theorems.
Gist of Idea
It is the second-order part of intuitionistic logic which actually negates some classical theorems
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 1.1)
Book Reference
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.2