
theorem LS2:
  SetPrimenumber 3 = {2}
  proof
A1: {2} is Subset of NAT by ZFMISC_1:31;
    for q being Nat holds q in {2} iff q < 3 & q is prime
    proof
      let q be Nat;
      hereby assume q in {2}; then
        q = 2 by TARSKI:def 1;
        hence q < 3 & q is prime by INT_2:28;
      end;
      assume
Z:    q < 3 & q is prime; then
      q < 2 + 1; then
      q <= 2 by NAT_1:13; then
      q = 0 or ... or q = 2;
      hence thesis by TARSKI:def 1,Z;
    end;
    hence thesis by A1,NEWTON:def 7;
  end;
