theorem Th3: :: CAT_5:3

for C1 being Category
for C2 being Subcategory of C1 st C1 is Subcategory of C2 holds
CatStr(# the carrier of C1, the carrier' of C1, the Source of C1, the Target of C1, the Comp of C1 #) = CatStr(# the carrier of C2, the carrier' of C2, the Source of C2, the Target of C2, the Comp of C2 #)