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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 2738 | . 2 ⊢ 𝐴 = 𝐴 | |
2 | elsng 4570 | . 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∈ {𝐴} ↔ 𝐴 = 𝐴)) | |
3 | 1, 2 | mpbiri 261 | 1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ {𝐴}) |
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