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| Mirrors > Home > MPE Home > Th. List > disjdif | Structured version Visualization version GIF version | ||
| Description: A class and its relative complement are disjoint. Theorem 38 of [Suppes] p. 29. (Contributed by NM, 24-Mar-1998.) |
| Ref | Expression |
|---|---|
| disjdif | ⊢ (𝐴 ∩ (𝐵 ∖ 𝐴)) = ∅ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | inss1 4237 | . 2 ⊢ (𝐴 ∩ 𝐵) ⊆ 𝐴 | |
| 2 | inssdif0 4374 | . 2 ⊢ ((𝐴 ∩ 𝐵) ⊆ 𝐴 ↔ (𝐴 ∩ (𝐵 ∖ 𝐴)) = ∅) | |
| 3 | 1, 2 | mpbi 230 | 1 ⊢ (𝐴 ∩ (𝐵 ∖ 𝐴)) = ∅ |
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