% Mizar problem: t65_zfmisc_1,zfmisc_1,836,27 
fof(t65_zfmisc_1,conjecture,(
    ! [A,B] : 
      ( k4_xboole_0(A,k1_tarski(B)) = A
    <=> ~ r2_hidden(B,A) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,dt_k1_tarski,dt_k4_xboole_0,l25_zfmisc_1,l28_zfmisc_1,symmetry_r1_xboole_0,t83_xboole_1]),
    [file(zfmisc_1,t65_zfmisc_1)]).

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(l25_zfmisc_1,axiom,(
    ! [A,B] : ~ ( r1_xboole_0(k1_tarski(A),B)
      & r2_hidden(A,B) ) ),
    file(zfmisc_1,l25_zfmisc_1),
    []).

fof(l28_zfmisc_1,axiom,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) ),
    file(zfmisc_1,l28_zfmisc_1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t83_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    []).