| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > elsni | Structured version Visualization version GIF version | ||
| Description: There is at most one element in a singleton. (Contributed by NM, 5-Jun-1994.) |
| Ref | Expression |
|---|---|
| elsni | ⊢ (𝐴 ∈ {𝐵} → 𝐴 = 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elsng 4640 | . 2 ⊢ (𝐴 ∈ {𝐵} → (𝐴 ∈ {𝐵} ↔ 𝐴 = 𝐵)) | |
| 2 | 1 | ibi 267 | 1 ⊢ (𝐴 ∈ {𝐵} → 𝐴 = 𝐵) |
| Copyright terms: Public domain | W3C validator |