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# Idempotency of entailment

Idempotency of entailment is a property of logical systems that states that one may derive the same consequences from many instances of a hypothesis as from just one. In sequent calculi this property can be captured by a structural rule called contraction and in such systems one may say that entailment is idempotent just in case contraction is an admissible rule.

Rule of Contraction: from

A,C,C -> B

is derived

A,C -> B.

Or in sequent calculus notation,

$frac\left\{Gamma,C,Cvdash B\right\}\left\{Gamma,Cvdash B\right\}$

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