theorem Th11: :: PRALG_2:11

for I being non empty set
for S being non empty non void ManySortedSign
for A being MSAlgebra-Family of I,S
for o being OperSymbol of S holds
( dom (doms (A ?. o)) = I & ( for i being Element of I holds (doms (A ?. o)) . i = Args (o,(A . i)) ) )