In deductive logic, we may make the following step:
( {Γ,P}⊨Q & {Γ,P}⊨¬Q ) ⇒ {Γ}⊨¬P
I've been trying to find examples of a proof that this inference follows, but I've struggled with my search. If anyone could point me in the right direction, or show me the proof, it would be much appreciated.
I would be particularly interested in a proof that doesn't use a deduction theorem to prove that a reductio as a logically permissible inferential step.