
theorem Th7:
  for f being continuous Function of R^1, R^1, g being PartFunc of
  REAL, REAL st f = g holds g is continuous
proof
  let f be continuous Function of R^1, R^1;
  let g be PartFunc of REAL, REAL;
  assume
A1: f = g;
  for x0 being Real st x0 in dom(g) holds g is_continuous_in x0
  by A1,Th6,TMAP_1:44,TOPMETR:17;
  hence thesis by FCONT_1:def 2;
end;
