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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 4676 | . 2 ⊢ (𝐴 ∈ V → 𝐴 ∈ {𝐴, 𝐵}) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ {𝐴, 𝐵} |
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