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
  a>0 & a<>1 & b>0 & b<>1 & c>0 implies log(a,c) = log(a,b)*log(b,c)
proof
  assume that
A1: a>0 and
A2: a<>1 and
A3: b>0 and
A4: b<>1 and
A5: c>0;
 a to_power (log(a,b)*log(b,c))
  = a to_power log(a,b) to_power log(b,c) by A1,Th33
    .= b to_power log(b,c) by A1,A2,A3,Def3
    .= c by A3,A4,A5,Def3;
  hence thesis by A1,A2,A5,Def3;
end;
