Classical logic can be embedded into intuitionistic logic. The double-negation translation N [0] turns any tautology of classical logic into a tautology of intuitionistic logic, so if θ ∧ ¬θ is provable with classical logic, N(θ) ∧ ¬N(θ) is provable with intuitionistic logic.

[0]: https://en.wikipedia.org/wiki/Double-negation_translation