theorem Th34:
  [:QC-WFF(Al),vSUB(Al):] c= dom QSub(Al)
proof
  let a be object;
  assume a in [:QC-WFF(Al),vSUB(Al):];
  then consider b,c being object such that
A1: b in QC-WFF(Al) and
A2: c in vSUB(Al) and
A3: a = [b,c] by ZFMISC_1:def 2;
  reconsider Sub = c as CQC_Substitution of Al by A2;
  reconsider p = b as Element of QC-WFF(Al) by A1;
A4: now
    set b = {};
    set a = [[p,Sub],b];
    assume not p is universal;
    then p,Sub PQSub b by SUBSTUT1:def 14;
    then a in QSub(Al) by SUBSTUT1:def 15;
    hence thesis by A3,FUNCT_1:1;
  end;
  now
    set b = ExpandSub(bound_in p,the_scope_of p, RestrictSub(bound_in p,p,Sub)
    );
    set a = [[p,Sub],b];
    assume p is universal;
    then p,Sub PQSub b by SUBSTUT1:def 14;
    then a in QSub(Al) by SUBSTUT1:def 15;
    hence thesis by A3,FUNCT_1:1;
  end;
  hence thesis by A4;
end;
