let P1, P2 be Probability of COM (Sigma,P); ( ( for B being set st B in Sigma holds
for C being thin of P holds P1 . (B \/ C) = P . B ) & ( for B being set st B in Sigma holds
for C being thin of P holds P2 . (B \/ C) = P . B ) implies P1 = P2 )
assume that
A84:
for B being set st B in Sigma holds
for C being thin of P holds P1 . (B \/ C) = P . B
and
A85:
for B being set st B in Sigma holds
for C being thin of P holds P2 . (B \/ C) = P . B
; P1 = P2
for x being object st x in COM (Sigma,P) holds
P1 . x = P2 . x
hence
P1 = P2
; verum