theorem
  f|SC = dom (f|SC) --> d implies f|SC is constant
proof
  assume
A1: f|SC = dom (f|SC) --> d;
  now
    let c;
    assume c in SC /\ dom f;
    then
A2: c in dom (f|SC) by RELAT_1:61;
    then f|SC/.c = d by A1,Th29;
    hence f/.c = d by A2,Th15;
  end;
  hence thesis by Th35;
end;
