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| Mirrors > Home > MPE Home > Th. List > snssi | Structured version Visualization version GIF version | ||
| Description: The singleton of an element of a class is a subset of the class. (Contributed by NM, 6-Jun-1994.) |
| Ref | Expression |
|---|---|
| snssi | ⊢ (𝐴 ∈ 𝐵 → {𝐴} ⊆ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | snssg 4783 | . 2 ⊢ (𝐴 ∈ 𝐵 → (𝐴 ∈ 𝐵 ↔ {𝐴} ⊆ 𝐵)) | |
| 2 | 1 | ibi 267 | 1 ⊢ (𝐴 ∈ 𝐵 → {𝐴} ⊆ 𝐵) |
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