Basic Probability Rule

#1
Hello friends,
Can anyone please give me any authentic resource (book/ literature review article/ any other useful documents ) of this rule. Also can you please let me know what is this rule called.

It doesn't necessarily have to be a chain rule. You can also consider,
P(A + B) = 1 - [ ( 1 - P(A)) * ( 1 - P(B)) ]

Thank you so much in advance.