@user525966 I don't know what you mean. I defined minimal logic for you before (what can be proven in my system without DNE), and that's obviously what the wikipedia article is referring to.

"minimal logic" is just a proper noun, and has nothing to do with minimality of rules, if that's what you're confused about.

They said that P1 to P4 gives classical logic, and P1 to P3 gives positive implicational logic, and P1 to P3 plus P4m gives minimal logic.

@user21820 Yeah was just unsure of the last part

couldn't tell if they meant p4 + p4m or just p4m after having subtracted p4

@user525966 Yup that's what their "adding instead" meant.