let Omega be non empty set ; :: thesis: for Sigma being SigmaField of Omega

for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

let Sigma be SigmaField of Omega; :: thesis: for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

let A, B be Event of Sigma; :: thesis: for P being Probability of Sigma holds P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

let P be Probability of Sigma; :: thesis: P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

P . (A \/ B) = (P . A) + (P . (B \ (A /\ B))) by Th37

.= (P . A) + ((P . B) - (P . (A /\ B))) by Th33, XBOOLE_1:17 ;

hence P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B)) ; :: thesis: verum

for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

let Sigma be SigmaField of Omega; :: thesis: for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

let A, B be Event of Sigma; :: thesis: for P being Probability of Sigma holds P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

let P be Probability of Sigma; :: thesis: P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B))

P . (A \/ B) = (P . A) + (P . (B \ (A /\ B))) by Th37

.= (P . A) + ((P . B) - (P . (A /\ B))) by Th33, XBOOLE_1:17 ;

hence P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B)) ; :: thesis: verum