% Mizar problem: t13_ordinal3,ordinal3,109,36 
fof(t13_ordinal3,conjecture,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => v3_ordinal1(k1_setfam_1(B)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_ordinal1,cc2_ordinal1,d6_ordinal2,dt_k1_setfam_1,dt_k1_zfmisc_1,dt_k2_ordinal2,dt_k6_ordinal2,dt_m1_subset_1,existence_m1_subset_1,rc1_ordinal1,reflexivity_r1_tarski,t3_subset,t8_ordinal3]),
    [file(ordinal3,t13_ordinal3)]).

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(d6_ordinal2,axiom,(
    ! [A] : k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A)) ),
    file(ordinal2,d6_ordinal2),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    []).

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

fof(dt_k2_ordinal2,axiom,(
    $true ),
    file(ordinal2,k2_ordinal2),
    []).

fof(dt_k6_ordinal2,axiom,(
    ! [A] : v3_ordinal1(k6_ordinal2(A)) ),
    file(ordinal2,k6_ordinal2),
    []).

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

fof(t8_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => k2_ordinal2(B) = B ) ) ),
    file(ordinal3,t8_ordinal3),
    []).