 reserve L for Quasi-Boolean_Algebra,
         x, y, z for Element of L;
 reserve L for Nelson_Algebra,
         a, b, c, d, x, y, z for Element of L;

theorem  :: (2.42)
  (a => b) => ((c => d) => ((a "/\" c) => (b "/\" d))) = Top L
  proof
A1: (a "/\" (a => b)) < b by Th17;
    (c "/\" (c => d)) < d by Th17; then
    (c "/\" (c => d)) "/\" (a "/\" (a => b)) < (b "/\" d) by Lm2,A1; then
    (c "/\" (c => d))"/\" a "/\" ((a => b)) < (d "/\" b)
      by LATTICES:def 7; then
    (a "/\" c "/\" (c => d)) "/\" ((a => b)) < (b "/\" d)
      by LATTICES:def 7; then
    (a "/\" c) "/\" ((c => d) "/\" (a => b)) < (b "/\" d)
      by LATTICES:def 7; then
    (c => d) "/\" (a => b) < ((a "/\" c) => (b "/\" d)) by Def4; then
    (a => b) < ((c => d) => ((a "/\" c) => (b "/\" d))) by Def4;
    hence thesis;
  end;
