Section DEDUCTION_THEOREM.
End DEDUCTION_THEOREM.

Lemma MP_preserves_truth (p : frm L) (q : frm L) (ps1 : list (frm L)) (ps2 : list (frm L)) (Gamma : ensemble (frm L))
(ENTAILS1 : forall Gamma, E.fromList ps1 \subseteq Gamma -> Gamma ⊨ Imp_frm p q)
(ENTAILS2 : forall Gamma, E.fromList ps2 \subseteq Gamma -> Gamma ⊨ p)
(INCL : E.fromList (ps1 ++ ps2) \subseteq Gamma)
: Gamma ⊨ q.