theorem Th163:
  G1 <=> G2 = (H1 <=> H2)/(x,y) iff G1 = H1/(x,y) & G2 = H2/(x,y)
proof
  G1 <=> G2 = (H1 <=> H2)/(x,y) iff G1 => G2 = (H1 => H2)/(x,y) & G2 => G1
  = (H2 => H1)/(x,y) by Th158;
  hence thesis by Th162;
end;
