reserve X,Y for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,h for Function;

theorem Th26:
  for f being Function, x being set st x in dom f holds f|{x} = {[ x,f.x]}
proof
  let f be Function, x be set such that
A1: x in dom f;
A2: x in {x} by TARSKI:def 1;
  dom(f|{x} qua Function) = dom f /\ {x} by RELAT_1:61
    .= {x} by A1,ZFMISC_1:46;
  hence f|{x} = {[x,(f|{x}).x]} by Th7
    .= {[x,f.x]} by A2,FUNCT_1:49;
end;
