% Mizar problem: t185_relat_1,relat_1,2587,50 
fof(t185_relat_1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C,D] : 
              ( ( k7_relat_1(A,C) = k7_relat_1(B,C)
                & k7_relat_1(A,D) = k7_relat_1(B,D) )
             => k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,dt_k2_xboole_0,dt_k7_relat_1,fc2_relat_1,idempotence_k2_xboole_0,t107_relat_1]),
    [file(relat_1,t185_relat_1)]).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(t107_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) ) ),
    file(relat_1,t107_relat_1),
    []).