
theorem LS3:
  SetPrimenumber 5 = {2, 3}
  proof
A1: {2, 3} is Subset of NAT by ZFMISC_1:32;
    for q being Nat holds q in {2,3} iff q < 5 & q is prime
    proof
      let q be Nat;
      hereby assume q in {2,3}; then
        q = 2 or q = 3 by TARSKI:def 2;
        hence q < 5 & q is prime by INT_2:28,PEPIN:41;
      end;
      assume
   Z: q < 5 & q is prime; then
      q < 4 + 1; then
      q <= 4 by NAT_1:13; then
      q = 0 or ... or q = 4;
      hence thesis by TARSKI:def 2,Z,INT_2:29;
    end;
    hence thesis by A1,NEWTON:def 7;
  end;
