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| Mirrors > Home > MPE Home > Th. List > velsn | Structured version Visualization version GIF version | ||
| Description: There is only one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15. (Contributed by NM, 21-Jun-1993.) |
| Ref | Expression |
|---|---|
| velsn | ⊢ (𝑥 ∈ {𝐴} ↔ 𝑥 = 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | vex 3484 | . 2 ⊢ 𝑥 ∈ V | |
| 2 | 1 | elsn 4641 | 1 ⊢ (𝑥 ∈ {𝐴} ↔ 𝑥 = 𝐴) |
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