Simplification

Transformation rules
Propositional calculus
Rules of inference Modus ponens Modus tollens Modus ponendo tollens Biconditional introduction Biconditional elimination Conjunction introduction Simplification Disjunction introduction Disjunction elimination Disjunctive syllogism Hypothetical syllogism Constructive dilemma Destructive dilemma Absorption Rules of replacement Associativity Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology
Predicate logic
Universal generalization Universal instantiation Existential generalization Existential instantiation

For other uses, see Simplification (disambiguation).

In propositional logic, simplification (equivalent to conjunction elimination) is a valid argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.

In formal language:

$A \and B \vdash A$

and

$A \and B \vdash B$

The argument has one premise, namely a conjunction, and one often uses simplification in longer arguments to derive one of the conjuncts.

An example in English:

It's raining and it's pouring.

Therefore it's raining.