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| Mirrors > Home > MPE Home > Th. List > snidg | Structured version Visualization version GIF version | ||
| Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 28-Oct-2003.) |
| Ref | Expression |
|---|---|
| snidg | ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ {𝐴}) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqid 2737 | . 2 ⊢ 𝐴 = 𝐴 | |
| 2 | elsng 4640 | . 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∈ {𝐴} ↔ 𝐴 = 𝐴)) | |
| 3 | 1, 2 | mpbiri 258 | 1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ {𝐴}) |
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