Simplification is a basic rule of inference in logic logic by which a proposition or formula is extracted from a conjunction. Simplifcation, which is also known as the conjunction elimination rule of inference (or ∧E), dictates that if "A and B" is true, then A is true (or, similarly, B is true).
Simplification may be formally presented as follows:
α ∧ β 
α
…and:
α ∧ β β