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 Th38:
  q in M & q in N & M is being_line & N is being_line implies ex X
  st M c= X & N c= X & X is being_plane
proof
  assume that
A1: q in M and
A2: q in N and
A3: M is being_line and
A4: N is being_line;
  consider a such that
A5: a<>q and
A6: a in N by A4,AFF_1:20;
A7: ex X st a in X & M c= X & X is being_plane by A3,Th36;
  N=Line(q,a) by A2,A4,A5,A6,AFF_1:24;
  hence thesis by A1,A5,A7,Th19;
end;
