theorem Th3: :: CARDFIL4:3

for X1, X2 being set
for S1 being Subset-Family of X1
for S2 being Subset-Family of X2 holds { s where s is Subset of [:X1,X2:] : ex s1, s2 being set st
( s1 in S1 & s2 in S2 & s = [:s1,s2:] ) } is Subset-Family of [:X1,X2:]