diff --git a/src/main/dune b/src/main/dune
index dc2cb0b7..948a0873 100644
--- a/src/main/dune
+++ b/src/main/dune
@@ -5,7 +5,7 @@
   (public_name sidekick)
   (package sidekick)
   (libraries containers sequence result msat sidekick.smt sidekick.smtlib
-             sidekick.dimacs)
+             sidekick.smt.th-ite sidekick.dimacs)
   (flags :standard -w +a-4-42-44-48-50-58-32-60@8
          -safe-string -color always -open Sidekick_util)
   (ocamlopt_flags :standard -O3 -color always
diff --git a/src/main/main.ml b/src/main/main.ml
index edb43c35..e2cb6869 100644
--- a/src/main/main.ml
+++ b/src/main/main.ml
@@ -119,6 +119,7 @@ let main () =
       | Smtlib ->
         [ Sidekick_th_bool.th_dynamic_tseitin;
           Sidekick_th_distinct.th;
+          Sidekick_th_ite.th;
         ] (* TODO: more theories *)
     in
     Sidekick_smt.Solver.create ~store_proof:!check ~theories ()
diff --git a/src/th-ite/Sidekick_th_ite.ml b/src/th-ite/Sidekick_th_ite.ml
new file mode 100644
index 00000000..176b2ea7
--- /dev/null
+++ b/src/th-ite/Sidekick_th_ite.ml
@@ -0,0 +1,113 @@
+
+(** {1 Theory for if-then-else} *)
+
+type 't ite_view =
+  | T_ite of 't * 't * 't
+  | T_bool of bool
+  | T_other of 't
+
+
+module type S = sig
+  type lit
+  type term
+
+  val th : Sidekick_smt.Theory.t
+end
+
+module type ARG = sig
+  module T : sig
+    type t
+    type state
+    val pp : t Fmt.printer
+    val equal : t -> t -> bool
+    val view_as_ite : t -> t ite_view
+
+    module Set : CCSet.S with type elt = t
+  end
+  module Lit : sig
+    type t
+    val term : t -> T.t
+    val atom : T.state -> ?sign:bool -> T.t -> t
+    val pp : t Fmt.printer
+  end
+end
+
+module Make(Arg : ARG with type T.state = Sidekick_smt.Term.state and type T.t = Sidekick_smt.Term.t)
+  : S with type lit = Arg.Lit.t and type term = Arg.T.t
+= struct
+  module Th = Sidekick_smt.Theory
+  module N = Th.CC_eq_class
+  module Expl = Th.CC_expl
+  module CC = Sidekick_smt.CC
+
+  open Arg
+  type lit = Lit.t
+  type term = T.t
+
+  type data = T.Set.t
+  (* associate to each class [t] the set of [ite a b c] where [a=t] *)
+
+  let pp_data = Fmt.(map T.Set.to_seq @@ seq ~sep:(return ",@ ") T.pp)
+
+  let key : (_,_,data) Sidekick_cc.Key.t = Sidekick_cc.Key.create
+      ~pp:pp_data ~name:"ite" ~eq:T.Set.equal ~merge:T.Set.union ()
+
+  type t = T.state
+
+  let on_merge (_st:t) (acts:Sidekick_smt.Theory.actions) n1 n2 e_n1_n2 : unit =
+    let (module A) = acts in
+    Log.debugf 5
+      (fun k->k "(@[th-ite.on_merge@ :c1 %a@ :c2 %a@])" N.pp n1 N.pp n2); 
+    (* check if [n1] has some [ite] parents, and if [n2] is true/false *)
+    let check_ n1 n2 =
+      match CC.Theory.get_data A.cc n1 key, T.view_as_ite (N.term n2) with
+      | Some set, T_bool n2_true ->
+        assert (not @@ T.Set.is_empty set);
+        T.Set.iter
+          (fun parent_1 -> match T.view_as_ite parent_1 with
+             | T_ite (a1,b1,c1) ->
+               let n_parent1 = CC.add_term A.cc parent_1 in
+               let expl = Expl.mk_list [e_n1_n2; Expl.mk_merge n1 (CC.add_term A.cc a1)] in
+               if n2_true then (
+                 (* [a1 = n1 = n2 = true] so [if a1 b1 c1 = b1] *)
+                 CC.Theory.merge A.cc n_parent1 (CC.add_term A.cc b1) expl
+               ) else (
+                 (* [a1 = n1 = n2 = false] so [if a1 b1 c1 = c1] *)
+                 CC.Theory.merge A.cc n_parent1 (CC.add_term A.cc c1) expl
+               )
+             | _ -> assert false)
+          set
+      | _ -> ()
+    in
+    check_ n1 n2;
+    check_ n2 n1;
+    ()
+
+  let on_new_term _ (acts:Sidekick_smt.Theory.actions) (t:T.t) =
+    let (module A) = acts in
+    match T.view_as_ite t with
+    | T_ite (a,_,_) ->
+      (* add [t] to parents of [a] *)
+      let n_a = CC.find A.cc @@ CC.add_term A.cc a in
+      CC.Theory.add_data A.cc n_a key (T.Set.singleton t)
+    | _ -> ()
+
+  let th =
+    Sidekick_smt.Theory.make ~name:"ite" ~create:(fun st->st)
+      ~on_merge ~final_check:(fun _ _ _ -> ())
+      ~on_new_term
+      ()
+
+end
+
+
+include Make(struct
+    module T = struct
+      include Sidekick_smt.Term
+      let[@inline] view_as_ite t = match view t with
+        | If (a,b,c) -> T_ite (a,b,c)
+        | Bool b -> T_bool b
+        | _ -> T_other t
+      end
+    module Lit = Sidekick_smt.Lit
+    end)
diff --git a/src/th-ite/dune b/src/th-ite/dune
new file mode 100644
index 00000000..d6cee8a8
--- /dev/null
+++ b/src/th-ite/dune
@@ -0,0 +1,8 @@
+
+
+(library
+  (name Sidekick_th_ite)
+  (public_name sidekick.smt.th-ite)
+  (libraries containers sidekick.smt)
+  (flags :standard -open Sidekick_util))
+