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| Mirrors > Home > MPE Home > Th. List > eldifsni | Structured version Visualization version GIF version | ||
| Description: Membership in a set with an element removed. (Contributed by NM, 10-Mar-2015.) |
| Ref | Expression |
|---|---|
| eldifsni | ⊢ (𝐴 ∈ (𝐵 ∖ {𝐶}) → 𝐴 ≠ 𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eldifsn 4786 | . 2 ⊢ (𝐴 ∈ (𝐵 ∖ {𝐶}) ↔ (𝐴 ∈ 𝐵 ∧ 𝐴 ≠ 𝐶)) | |
| 2 | 1 | simprbi 496 | 1 ⊢ (𝐴 ∈ (𝐵 ∖ {𝐶}) → 𝐴 ≠ 𝐶) |
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