% Mizar problem: t148_pboole,pboole,1880,62 
fof(t148_pboole,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ( ! [E] : 
                    ( m1_pboole(E,A)
                   => ( r1_pboole(A,E,D)
                    <=> ( r1_pboole(A,E,B)
                        & r1_pboole(A,E,C) ) ) )
               => r6_pboole(A,D,k3_pboole(A,B,C)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_pboole,dt_k3_pboole,dt_m1_pboole,existence_m1_pboole,idempotence_k3_pboole,rc1_funct_1,rc3_pboole,rc5_funct_1,redefinition_r6_pboole,reflexivity_r6_pboole,symmetry_r6_pboole,t147_pboole,t8_pboole]),
    [file(pboole,t148_pboole)]).

fof(commutativity_k3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k3_pboole(A,B,C) = k3_pboole(A,C,B) ) ),
    file(pboole,k3_pboole),
    []).

fof(dt_k3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => m1_pboole(k3_pboole(A,B,C),A) ) ),
    file(pboole,k3_pboole),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

fof(idempotence_k3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => k3_pboole(A,B,B) = B ) ),
    file(pboole,k3_pboole),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t147_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ( ! [D] : 
                ( m1_pboole(D,A)
               => ( r1_pboole(A,D,C)
                <=> r1_pboole(A,D,B) ) )
           => r6_pboole(A,C,B) ) ) ) ),
    file(pboole,t147_pboole),
    []).

fof(t8_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r1_pboole(A,B,k3_pboole(A,C,D))
              <=> ( r1_pboole(A,B,C)
                  & r1_pboole(A,B,D) ) ) ) ) ) ),
    file(pboole,t8_pboole),
    []).