% Mizar problem: t29_sysrel,sysrel,374,20 
fof(t29_sysrel,conjecture,(
    ! [A] : k5_relat_1(k6_relat_1(A),k6_relat_1(A)) = k6_relat_1(A) ),
    inference(mizar_bg_added,[status(thm)],[dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k5_relat_1,dt_k6_relat_1,dt_m1_subset_1,existence_m1_subset_1,reflexivity_r1_tarski,t3_subset,t71_relat_1,t77_relat_1]),
    [file(sysrel,t29_sysrel)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

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(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(t71_relat_1,axiom,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    []).

fof(t77_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k5_relat_1(k6_relat_1(A),B) = B ) ) ),
    file(relat_1,t77_relat_1),
    []).