Article SUBSET, MML version 4.99.1005

:: SUBSET:th 1
theorem
for b1, b2 being set
      st b1 in b2
   holds b1 is Element of b2;

:: SUBSET:th 3
theorem
for b1, b2 being set holds
   b1 is Element of bool b2
iff
   b1 c= b2;

:: SUBSET:th 4
theorem
for b1, b2, b3 being set
      st b1 in b2 & b2 is Element of bool b3
   holds b1 is Element of b3;

:: SUBSET:th 5
theorem
for b1, b2, b3 being set
      st b1 in b2 & b2 is Element of bool b3
   holds b3 is not empty;