% Mizar problem: t83_extreal2,extreal2,1991,16 
fof(t83_extreal2,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => k1_extreal2(A,B) = k1_extreal2(B,A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k1_extreal2,idempotence_k1_extreal2,existence_m1_subset_1,dt_k1_extreal2,dt_k3_supinf_1,dt_m1_subset_1]),
    [file(extreal2,t83_extreal2)]).

fof(commutativity_k1_extreal2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k1_extreal2(A,B) = k1_extreal2(B,A) ) ),
    file(extreal2,k1_extreal2),
    []).

fof(idempotence_k1_extreal2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k1_extreal2(A,A) = A ) ),
    file(extreal2,k1_extreal2),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_k1_extreal2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k1_extreal2(A,B),k3_supinf_1) ) ),
    file(extreal2,k1_extreal2),
    []).

fof(dt_k3_supinf_1,axiom,(
    $true ),
    file(supinf_1,k3_supinf_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).