% Mizar problem: t9_wellord2,wellord2,191,56 
fof(t9_wellord2,conjecture,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => v2_wellord1(k1_wellord2(B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_ordinal1,cc2_ordinal1,commutativity_k3_xboole_0,d6_wellord1,dt_k1_wellord2,dt_k1_zfmisc_1,dt_k2_wellord1,dt_k2_zfmisc_1,dt_k3_xboole_0,dt_m1_subset_1,existence_m1_subset_1,idempotence_k3_xboole_0,rc1_ordinal1,reflexivity_r1_tarski,t32_wellord1,t3_subset,t7_wellord2,t8_wellord2]),
    [file(wellord2,t9_wellord2)]).

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(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_k1_wellord2,axiom,(
    ! [A] : v1_relat_1(k1_wellord2(A)) ),
    file(wellord2,k1_wellord2),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

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

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

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

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

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t32_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v2_wellord1(B)
       => v2_wellord1(k2_wellord1(B,A)) ) ) ),
    file(wellord1,t32_wellord1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

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

fof(t8_wellord2,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_wellord1(k1_wellord2(B),A) = k1_wellord2(A) ) ),
    file(wellord2,t8_wellord2),
    []).