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| Mirrors > Home > MPE Home > Th. List > inidm | Structured version Visualization version GIF version | ||
| Description: Idempotent law for intersection of classes. Theorem 15 of [Suppes] p. 26. (Contributed by NM, 5-Aug-1993.) |
| Ref | Expression |
|---|---|
| inidm | ⊢ (𝐴 ∩ 𝐴) = 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | anidm 564 | . 2 ⊢ ((𝑥 ∈ 𝐴 ∧ 𝑥 ∈ 𝐴) ↔ 𝑥 ∈ 𝐴) | |
| 2 | 1 | ineqri 4212 | 1 ⊢ (𝐴 ∩ 𝐴) = 𝐴 |
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