Simplification rule (Logic)

From Conservapedia

The simplification rule in logic states that where a conjunction of two variables is true then both variables are true individually. In plainer English this means that where a statement using "and" is true the separate parts of the statement are true on their own.

For example if the following is true:

John has an apple and an orange

then the two following statements are also true:

John has an apple

and

John has an orange