reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);
reserve s,t for bound_QC-variable of A;
reserve F,G,H,H1 for Element of QC-WFF(A);
reserve x,y,z for bound_QC-variable of A,
  k,n,m for Nat,
  P for ( QC-pred_symbol of k, A),
  V for QC-variable_list of k, A;

theorem Th46:
  F is_immediate_constituent_of All(x,H) iff F = H
proof
  thus F is_immediate_constituent_of All(x,H) implies F = H
  proof
    All(x,H) is universal;
    then
A1: (@All(x,H).1)`1 = 3 by QC_LANG1:18;
A2:  All(x,H) <> 'not' F by A1,QC_LANG1:18,def 19;
A3: not ex G st All(x,H) = F '&' G or All(x,H) = G '&' F
      by A1,QC_LANG1:18,def 20;
    assume All(x,H) = 'not' F or (ex H1 st All(x,H) = F '&' H1 or All(x,H) =
    H1 '&' F) or ex y st All(x,H) = All(y,F);
    hence thesis by A2,A3,Th5;
  end;
  thus thesis;
end;
