reserve A for QC-alphabet;
reserve p, q, r, s, p1, q1 for Element of CQC-WFF(A),
  X, Y, Z, X1, X2 for Subset of CQC-WFF(A),
  h for QC-formula of A,
  x, y for bound_QC-variable of A,
  n for Element of NAT;

theorem
  p <==> q implies Ex(x,p) <==> Ex(x,q)
proof
  assume p <==> q;
  then 'not' p <==> 'not' q by Lm5;
  then All(x,'not' p) <==> All(x,'not' q) by Th58;
  then
A1: 'not' All(x,'not' p) <==> 'not' All(x,'not' q) by Lm5;
  Ex(x,p) = 'not' All(x,'not' p) by QC_LANG2:def 5;
  hence thesis by A1,QC_LANG2:def 5;
end;
