theorem Th46:
  c in dom f & d = f/.c iff [c,d] in f
proof
  thus c in dom f & d = f/.c implies [c,d] in f
  proof
    assume that
A1: c in dom f and
A2: d = f/.c;
    d = (f qua Function).c by A1,A2,PARTFUN1:def 6;
    hence thesis by A1,FUNCT_1:1;
  end;
  assume [c,d] in f;
  then c in dom f & d = (f qua Function).c by FUNCT_1:1;
  hence thesis by PARTFUN1:def 6;
end;
