In classical propositional logic and in first-order logic (with suitable side conditions on free variables), assuming an extra hypothesis φ is equivalent to proving the implication φ → ψ. Fails in logics lacking contraction.
In classical propositional logic and in first-order logic (with suitable side conditions on free variables), assuming an extra hypothesis φ is equivalent to proving the implication φ → ψ. Fails in logics lacking contraction.