:: SUBSET semantic presentation
theorem Th1: :: SUBSET:1
for b
1, b
2 being
set holds
( b
1 in b
2 implies b
1 is
Element of b
2 )
theorem Th2: :: SUBSET:2
theorem Th3: :: SUBSET:3
for b
1, b
2 being
set holds
( b
1 is
Subset of b
2 iff b
1 c= b
2 )
theorem Th4: :: SUBSET:4
for b
1, b
2, b
3 being
set holds
( b
1 in b
2 & b
2 is
Subset of b
3 implies b
1 is
Element of b
3 )
theorem Th5: :: SUBSET:5
for b
1, b
2, b
3 being
set holds
not ( b
1 in b
2 & b
2 is
Subset of b
3 & b
3 is
empty )