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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 ∩ 𝐴 ) = 𝐴

Proof

Step Hyp Ref Expression
1 anidm ⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝑥 ∈ 𝐴 ) ↔ 𝑥 ∈ 𝐴 )
2 1 ineqri ⊢ ( 𝐴 ∩ 𝐴 ) = 𝐴