How to prove Law of excluded middle using 10 axioms of Intuitionistic logic

Question

How to prove Law of excluded middle using 10 axioms of Intuitionistic logic?

Answer 1

The Law of the Excluded Middle cannot be proved within intuitionistic propositional logic: $p\lor \lnot p$,

just as double-negation elimination cannot be proved in the said system. I.e. Intuitionistic logic does not recognize that $\lnot \lnot p \equiv p.$

See Intuitionistic Logic.