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Metamath Proof Explorer

Theorem inidm

Description: Idempotent law for intersection of classes. Theorem 15 of Suppes p. 26. (Contributed by NM, 5-Aug-1993)

Ref Expression
Assertion inidm 
|- ( A i^i A ) = A

Proof

Step Hyp Ref Expression
1 anidm 
 |-  ( ( x e. A /\ x e. A ) <-> x e. A )
2 1 ineqri 
 |-  ( A i^i A ) = A