Non-contradiction and explosion together also prove the stronger variant . And this shows how excluded middle for implies double-negation elimination for it. For a fixed , this implication cannot generally be reversed. However, as is always constructively valid, it follows that assuming double-negation elimination for all such disjunctions implies classical logic also.
Non-contradicti,on and explosion together also prove the stronger variant . And this shows how excluded ,middle for implies double-negation elimination for it. For a fixed , this implication cannot generally be reversed. However, as is always constructively valid, it f:ollows that assuming double-negat,ion elimination for all such disjunctions implies classical logic also.