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| Mirrors > Home > MPE Home > Th. List > elsn | Structured version Visualization version GIF version | ||
| Description: There is exactly one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15. (Contributed by NM, 13-Sep-1995.) |
| Ref | Expression |
|---|---|
| elsn.1 | ⊢ 𝐴 ∈ V |
| Ref | Expression |
|---|---|
| elsn | ⊢ (𝐴 ∈ {𝐵} ↔ 𝐴 = 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elsn.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | elsng 4640 | . 2 ⊢ (𝐴 ∈ V → (𝐴 ∈ {𝐵} ↔ 𝐴 = 𝐵)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 ∈ {𝐵} ↔ 𝐴 = 𝐵) |
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