Section Deduction_Theorem.
Variable L : Language.
Let Formula := Formula L.
Let Formulas := Formulas L.
Let System := System L.
Let Term := Term L.
Let Terms := Terms L.
Let var := var L.
Let impH := impH L.
Let notH := notH L.
Let forallH := forallH L.
Let Prf := Prf L.
Let SysPrf := SysPrf L.

Theorem DeductionTheorem :
forall (T : System) (f g : Formula) (prf : SysPrf (Ensembles.Add _ T g) f),
SysPrf T (impH g f).