
theorem AZ1:
  for a be non weightless positive Real, b be positive Real holds
  log (a,b) = 1 iff a = b
  proof
    let a be non weightless positive Real, b be positive Real;
    A1: a <> 1 by TA1;
    log (a,b) = 1 implies a = b
    proof
      assume log (a,b) = 1; then
      b = a to_power 1;
      hence thesis;
    end;
    hence thesis by A1,POWER:52;
  end;
