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;

theorem Th32:
  F => G = F1 => G1 implies F = F1 & G = G1
proof
  assume F => G = F1 => G1;
  then
A1: F '&' 'not' G = F1 '&' 'not' G1 by FINSEQ_1:33;
  hence F = F1 by Th30;
  'not' G = 'not' G1 by A1,Th30;
  hence thesis by FINSEQ_1:33;
end;
