theorem Th28:
  not y in still_not-bound_in All(x,p) implies v.(y|a).(x|a)|
  still_not-bound_in p = v.(x|a)|still_not-bound_in p
proof
A1: v.(y|a).(x|a) = v+*((y|a)+*(x|a)) by FUNCT_4:14;
  assume
A2: not y in still_not-bound_in All(x,p);
  now
    assume
A3: x <> y;
    dom (x|a) = {x} & dom (y|a) = {y};
    then v.(y|a).(x|a) = v+*((x|a)+*(y|a)) by A1,A3,FUNCT_4:35,ZFMISC_1:11;
    then
A4: v.(y|a).(x|a) = v+*(x|a)+*(y|a) by FUNCT_4:14;
    not y in (still_not-bound_in p) \ {x} by A2,QC_LANG3:12;
    then not y in still_not-bound_in p by A3,ZFMISC_1:56;
    hence thesis by A4,Th26;
  end;
  hence thesis by A1;
end;
