Article BOOLE, MML version 4.99.1005

:: BOOLE:th 1
theorem
for b1 being set holds
   b1 \/ {} = b1;

:: BOOLE:th 2
theorem
for b1 being set holds
   b1 /\ {} = {};

:: BOOLE:th 3
theorem
for b1 being set holds
   b1 \ {} = b1;

:: BOOLE:th 4
theorem
for b1 being set holds
   {} \ b1 = {};

:: BOOLE:th 5
theorem
for b1 being set holds
   b1 \+\ {} = b1;

:: BOOLE:th 7
theorem
for b1, b2 being set
      st b1 in b2
   holds b2 is not empty;

:: BOOLE:th 8
theorem
for b1, b2 being set
      st b1 is empty & b1 <> b2
   holds b2 is not empty;