reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve p for Prime;

theorem Th48:
  for a, b, c being Real st c > 1 & c to_power a = c to_power b holds a = b
  proof
    let a,b,c be Real such that
A1: c > 1 and
A2: c to_power a = c to_power b;
    assume a <> b;
    then a < b or a > b by XXREAL_0:1;
    hence thesis by A1,A2,POWER:39;
  end;
