Simplification

Rules of inference
Propositional calculus
Modus ponens Modus tollens Modus ponendo tollens Conjunction introduction Simplification Disjunction introduction Disjunction elimination Disjunctive syllogism Hypothetical syllogism Constructive dilemma Destructive dilemma Biconditional introduction Biconditional elimination
Predicate calculus
Universal generalization Universal instantiation Existential generalization Existential instantiation

For other uses, see Simplification (disambiguation).

In mathematical logic, simplification (equivalent to conjunction elimination) is a valid argument 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:

$A \and B \vdash A$

or

$A \and B \vdash B$

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.