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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 4685 | . 2 ⊢ (𝐴 ∈ (𝐵 ∖ {𝐶}) ↔ (𝐴 ∈ 𝐵 ∧ 𝐴 ≠ 𝐶)) | |
2 | 1 | simprbi 500 | 1 ⊢ (𝐴 ∈ (𝐵 ∖ {𝐶}) → 𝐴 ≠ 𝐶) |
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