Rule of Simplification/Proof Rule

Proof Rule
The rule of simplification is a valid argument in types of logic dealing with conjunctions $\land$.

This includes propositional logic and predicate logic, and in particular natural deduction.

As a proof rule it is expressed in either of the two forms:
 * $(1): \quad$ If we can conclude $\phi \land \psi$, then we may infer $\phi$.
 * $(2): \quad$ If we can conclude $\phi \land \psi$, then we may infer $\psi$.

It can be written:
 * $\ds {\phi \land \psi \over \phi} \land_{e_1} \qquad \qquad {\phi \land \psi \over \psi} \land_{e_2}$

Also see

 * This is a rule of inference of the following proof system:
 * Definition:Natural Deduction


 * Rule of Conjunction