If we have $A$ which is dependent on $B$,$C$, and $D$, (all binary: True / False) then: $P(A=T,B=T,C=T) = P(A=T,B=T,C=T,D=T) + P(A=T,B=T,C=T,D=F)$.
Why is it incorrect if we apply the same logic to the following conditional probability:
$P(A=T| B=T,C=T) = P(A=T|B=T,C=T,D=T) + P(A=T|B=T,C=T,D=F)$
I kind of see why it's incorrect, but can we show it mathematically?