theorem Th63:
  {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10} = {x2,x3,x4,x5,x6,x7,x8,x9,x10} \/ {x1}
proof
  now
    let x be object;
A1: x in {x1} iff x=x1 by TARSKI:def 1;
    x=x2 or x=x3 or x=x4 or x=x5 or x=x6 or x=x7 or x=x8 or x=x9 or x=x10
    or x=x1 iff x in {x2,x3,x4,x5,x6,x7,x8,x9,x10} or x = x1
      by ENUMSET1:def 7;
    hence x in {x1,x2,x3,x4,x5,x6,x7,x8,x9,x10} iff x in {x2,x3,x4,x5,x6,
    x7,x8,x9,x10} \/ {x1} by A1,ENUMSET1:def 8,XBOOLE_0:def 3;
  end;
  hence thesis by TARSKI:2;
end;
