for Omega being non empty set
for Sigma being SigmaField of Omega
for P being Probability of Sigma
for E, F being Subset-Family of Omega st E is non empty Subset of Sigma & E is intersection_stable & F is non empty Subset of Sigma & F is intersection_stable & ( for p, q being Event of Sigma st p in E & q in F holds
p,q are_independent_respect_to P ) holds
for u, v being Event of Sigma st u in sigma E & v in sigma F holds
u,v are_independent_respect_to P