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
  H is conditional implies H = (the_antecedent_of H) => the_consequent_of H
proof
  assume
A1: H is conditional;
  then ex F st H = (the_antecedent_of H) => F by Def35;
  hence thesis by A1,Def36;
end;
