This is the way my text explains Nested If statements...

Nested, If/ElseIf/Else, and Case Selection Structures
Nested Selection Structures
You use the selection structure when you want a procedure to make a decision and then select one of two paths—either the true path or the false path—based on the result of that decision
Both paths in a selection structure can include instructions that declare and initialize variables, perform calculations, and so on
Both also can include other selection structures
When either a selection structure’s true path or its false path contains another selection structure, the inner selections structure is referred to as a nested selection structure, because I is contained (nested) within the outer selection structure
You use a nested selection structure when more than one decision must be made before the appropriate action can be taken
Assume you want to create a procedure that determines whether a person can vote, and then, based on the result of that determination, displays one of three messages
The person’s voter registration status is important only after his or her age is determined
You can think of the decision regarding the age as the primary decision, and the decision regarding the registration status as being the secondary decision, because whether the registration decision needs to be made by the outer selection structure, while the secondary decision is always made by the inner (nested) selection structure
The lines connecting the selection structures in the pseudocode and code are included in the figure to help you see which clauses are related to each other
The procedure begins by declaring the variables and then getting the age from the user
The condition in the outer selection structure then checks whether the age is greater than or equal to 18
If the condition is false, it means that the person is not old enough to vote
In that case, only one message—the “You are too young to vote.” message—is appropriate
After the message is displayed, both the outer selection structure and the procedure end
If the outer selection structure’s condition is true, it means that the person is old enough to vote
If he or she is registered, the instruction in the nested selection structure’s true path displays the “You can vote” message
Otherwise, the false path displays the “You need to register before you can vote” message
After the appropriate message is displayed, both selection structures and the procedure end
The nested selection structure in this procedure is processed only when the outer selection structure’s condition is true
The new example first declares the necessary variables and then gets the age from the user
However, rather than checking whether the age is greater than or equal to 18, the outer selection structure in this version checks whether the age is less than 18
If the condition is true, the instruction in the outer selection structure’s true path displays a message
If the condition is false, the instructions first get the registration status from the user, and then use a nested selection structure to determine whether the person is registered
Then it displays a message
Otherwise, it displays another message
The nested selection structure in this version is processed only when the outer selection is false
Both versions of the voter eligibility procedure produce the same results
Neither version is better than the other
Each simply represents a different way of solving he same problem