% Mizar problem: t27_wellord1,wellord1,407,29 
fof(t27_wellord1,conjecture,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(k2_wellord1(C,B),A) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xboole_0,d6_wellord1,dt_k2_wellord1,dt_k2_zfmisc_1,dt_k3_xboole_0,idempotence_k3_xboole_0,t26_wellord1]),
    [file(wellord1,t27_wellord1)]).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d6_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B)) ) ),
    file(wellord1,d6_wellord1),
    []).

fof(dt_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(t26_wellord1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(C,k3_xboole_0(A,B)) ) ),
    file(wellord1,t26_wellord1),
    []).