% Mizar problem: t12_amistd_3,amistd_3,299,24 
fof(t12_amistd_3,conjecture,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k2_wellord2(k1_wellord2(A)) = A ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_amistd_1,cc1_ordinal1,cc2_ordinal1,d2_wellord2,dt_k1_wellord2,dt_k2_wellord2,rc1_ordinal1,t48_wellord1,t7_wellord2]),
    [file(amistd_3,t12_amistd_3)]).

fof(cc1_amistd_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_1(A)
        & v1_setfam_1(A) ) ) ),
    file(amistd_1,cc1_amistd_1),
    []).

fof(cc1_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

fof(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

fof(d2_wellord2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
       => ! [B] : 
            ( v3_ordinal1(B)
           => ( B = k2_wellord2(A)
            <=> r4_wellord1(A,k1_wellord2(B)) ) ) ) ) ),
    file(wellord2,d2_wellord2),
    []).

fof(dt_k1_wellord2,axiom,(
    ! [A] : v1_relat_1(k1_wellord2(A)) ),
    file(wellord2,k1_wellord2),
    []).

fof(dt_k2_wellord2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v3_ordinal1(k2_wellord2(A)) ) ),
    file(wellord2,k2_wellord2),
    []).

fof(rc1_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(t48_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => r4_wellord1(A,A) ) ),
    file(wellord1,t48_wellord1),
    []).

fof(t7_wellord2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v2_wellord1(k1_wellord2(A)) ) ),
    file(wellord2,t7_wellord2),
    []).