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| Mirrors > Home > MPE Home > Th. List > elpri | Structured version Visualization version GIF version | ||
| Description: If a class is an element of a pair, then it is one of the two paired elements. (Contributed by Scott Fenton, 1-Apr-2011.) |
| Ref | Expression |
|---|---|
| elpri | ⊢ (𝐴 ∈ {𝐵, 𝐶} → (𝐴 = 𝐵 ∨ 𝐴 = 𝐶)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elprg 4648 | . 2 ⊢ (𝐴 ∈ {𝐵, 𝐶} → (𝐴 ∈ {𝐵, 𝐶} ↔ (𝐴 = 𝐵 ∨ 𝐴 = 𝐶))) | |
| 2 | 1 | ibi 267 | 1 ⊢ (𝐴 ∈ {𝐵, 𝐶} → (𝐴 = 𝐵 ∨ 𝐴 = 𝐶)) |
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