
theorem th5:
  for p,q,r be boolean object holds
    p => q => (p => r => (p => (q '&' r))) = TRUE
  proof
    let p,q,r be boolean object;
A1: p = TRUE or p = FALSE by XBOOLEAN:def 3;
A2: q = TRUE or q = FALSE by XBOOLEAN:def 3;
    r = TRUE or r = FALSE by XBOOLEAN:def 3;
    hence thesis by A1,A2;
  end;
