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Mirrors > Home > MPE Home > Th. List > elsni | Structured version Visualization version GIF version |
Description: There is at most one element in a singleton. (Contributed by NM, 5-Jun-1994.) |
Ref | Expression |
---|---|
elsni | ⊢ (𝐴 ∈ {𝐵} → 𝐴 = 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elsng 4581 | . 2 ⊢ (𝐴 ∈ {𝐵} → (𝐴 ∈ {𝐵} ↔ 𝐴 = 𝐵)) | |
2 | 1 | ibi 266 | 1 ⊢ (𝐴 ∈ {𝐵} → 𝐴 = 𝐵) |
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