reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;

theorem
  Free (p <=> q) = Free p \/ Free q
proof
  thus Free (p <=> q) = Free (p => q) \/ Free (q => p) by Th61
    .= Free p \/ Free q \/ Free (q => p) by Th64
    .= Free p \/ Free q \/ (Free q \/ Free p) by Th64
    .= Free p \/ Free q \/ Free q \/ Free p by XBOOLE_1:4
    .= Free p \/ (Free q \/ Free q) \/ Free p by XBOOLE_1:4
    .= Free p \/ Free p \/ Free q by XBOOLE_1:4
    .= Free p \/ Free q;
end;
