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| Mirrors > Home > MPE Home > Th. List > snssd | Structured version Visualization version GIF version | ||
| Description: The singleton of an element of a class is a subset of the class (deduction form). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
| Ref | Expression |
|---|---|
| snssd.1 | ⊢ (𝜑 → 𝐴 ∈ 𝐵) |
| Ref | Expression |
|---|---|
| snssd | ⊢ (𝜑 → {𝐴} ⊆ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | snssd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝐵) | |
| 2 | snssi 4808 | . 2 ⊢ (𝐴 ∈ 𝐵 → {𝐴} ⊆ 𝐵) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → {𝐴} ⊆ 𝐵) |
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