reserve AS for AffinSpace;
reserve a,b,c,d,a9,b9,c9,d9,p,q,r,x,y for Element of AS;
reserve A,C,K,M,N,P,Q,X,Y,Z for Subset of AS;

theorem Th25:
  X is being_plane & Y is being_plane & a in X & b in X & c in X &
  a in Y & b in Y & c in Y & not LIN a,b,c implies X = Y
proof
  assume that
A1: X is being_plane & Y is being_plane and
A2: a in X & b in X and
A3: c in X and
A4: a in Y & b in Y and
A5: c in Y and
A6: not LIN a,b,c;
  assume
A7: not thesis;
  a<>b by A6,AFF_1:7;
  then
A8: X /\ Y is being_line by A1,A2,A4,A7,Th24;
A9: c in X /\ Y by A3,A5,XBOOLE_0:def 4;
  a in X /\ Y & b in X /\ Y by A2,A4,XBOOLE_0:def 4;
  hence contradiction by A6,A8,A9,AFF_1:21;
end;
