% Mizar problem: t1_subset,subset,26,31 
fof(t1_subset,conjecture,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d1_xboole_0,d2_subset_1,d5_xboole_0,dt_k1_xboole_0,dt_m1_subset_1,existence_m1_subset_1,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0]),
    [file(subset,t1_subset)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
       => ( m1_subset_1(B,A)
        <=> r2_hidden(B,A) ) )
      & ( v1_xboole_0(A)
       => ( m1_subset_1(B,A)
        <=> v1_xboole_0(B) ) ) ) ),
    file(subset_1,d2_subset_1),
    []).

fof(d5_xboole_0,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
    <=> A = k1_xboole_0 ) ),
    file(xboole_0,d5_xboole_0),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).