reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem
  { p where p is Prime: 1 + p + p|^2 + p|^3 + p|^4 is square } = {3}
  proof
    set A = { p where p is Prime: 1 + p + p|^2 + p|^3 + p|^4 is square };
    thus A c= {3}
    proof
      let x be object;
      assume x in A;
      then ex p being Prime st x = p & 1 + p + p|^2 + p|^3 + p|^4 is square;
      then x = 3 by Th86;
      hence thesis by TARSKI:def 1;
    end;
    let p be object;
    assume p in {3};
    then
A1: p = 3 by TARSKI:def 1;
    then reconsider p as Prime by XPRIMES1:3;
    1 + p + p|^2 + p|^3 + p|^4 is square by A1,Th86;
    hence thesis;
  end;
