reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;
reserve F,G for Cardinal-Function;
reserve A,B for set;

theorem Th60:
  x in dom f & y in f.x implies x .--> y in sproduct f
proof
  assume that
A1: x in dom f and
A2: y in f.x;
A3: dom(x .--> y) c= dom f by A1,ZFMISC_1:31;
  now
    let z be object;
    assume z in dom(x .--> y);
    then z = x by TARSKI:def 1;
    hence (x .--> y).z in f.z by A2,FUNCOP_1:72;
  end;
  hence thesis by A3,Def9;
end;
