reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;
reserve L,L0,L1,L2 for Element of line_of_REAL n;
reserve P,P0,P1,P2 for Element of plane_of_REAL n;

theorem
  P1 is being_plane & P1 c= P2 implies P1 = P2
proof
  assume that
A1: P1 is being_plane and
A2: P1 c= P2;
  consider x1,x2,x3 be Element of REAL n such that
A3: x2 - x1, x3 - x1 are_lindependent2 & P1 = plane(x1,x2,x3) by A1;
A4: x3 in plane(x1,x2,x3) by Th82;
  x1 in plane(x1,x2,x3) & x2 in plane(x1,x2,x3) by Th82;
  hence thesis by A2,A3,A4,Th92;
end;
