Section DEDUCTION_THEOREM.
End DEDUCTION_THEOREM.
#[local] Existing Instance V.vec_isSetoid.

Lemma for_All_I (x : ivar) (p : frm L) (Gamma : ensemble (frm L))
(FRESH : is_not_free_in_frms x Gamma)
(PROVE : Gamma \proves p)
: Gamma \proves All_frm x p.