reserve X for set;

theorem Th15:
  for A being Subset of X, f being X-defined Relation holds
    f|A` = f|(dom f \ A)
proof
   let A be Subset of X, f be X-defined Relation;
   f|A` = (f|dom f)|A`
    .= f|(dom f /\ A`) by RELAT_1:71
    .= f|(dom f /\ (X \ A)) by SUBSET_1:def 4
    .= f|((dom f /\ X) \ A) by XBOOLE_1:49;
   hence f|A` = f|(dom f \ A) by XBOOLE_1:28;
end;
