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| Mirrors > Home > MPE Home > Th. List > prid1 | Structured version Visualization version GIF version | ||
| Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 24-Jun-1993.) |
| Ref | Expression |
|---|---|
| prid1.1 | ⊢ 𝐴 ∈ V |
| Ref | Expression |
|---|---|
| prid1 | ⊢ 𝐴 ∈ {𝐴, 𝐵} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | prid1.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | prid1g 4760 | . 2 ⊢ (𝐴 ∈ V → 𝐴 ∈ {𝐴, 𝐵}) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ {𝐴, 𝐵} |
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