reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;
reserve F,F1,G,G1,H,H1 for ZF-formula;
reserve sq,sq9 for FinSequence;
reserve L,L9 for FinSequence;
reserve j,j1 for Element of NAT;

theorem Th77:
  H is_subformula_of x 'in' y iff H = x 'in' y
proof
  thus H is_subformula_of x 'in' y implies H = x 'in' y
  proof
    assume
A1: H is_subformula_of x 'in' y;
    assume H <> x 'in' y;
    then H is_proper_subformula_of x 'in' y by A1;
    then ex F st F is_immediate_constituent_of x 'in' y by Th63;
    hence contradiction by Th51;
  end;
  assume H = x 'in' y;
  hence thesis by Th59;
end;
