reserve x for set;
reserve a, b, c, d, e for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p for Rational;

theorem Th33:
  a > 0 implies a to_power b to_power c = a to_power (b * c)
proof
  assume
A1: a > 0;
then A2: a #R b > 0 by PREPOWER:81;
 a #R b #R c = a #R (b * c) by A1,PREPOWER:91;
then  a #R b #R c = a to_power (b * c) by A1,Def2;
then  a #R b to_power c = a to_power (b * c) by A2,Def2;
  hence thesis by A1,Def2;
end;
