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| Mirrors > Home > MPE Home > Th. List > elexi | Structured version Visualization version GIF version | ||
| Description: If a class is a member of another class, then it is a set. Inference associated with elex 3501. (Contributed by NM, 11-Jun-1994.) |
| Ref | Expression |
|---|---|
| elexi.1 | ⊢ 𝐴 ∈ 𝐵 |
| Ref | Expression |
|---|---|
| elexi | ⊢ 𝐴 ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elexi.1 | . 2 ⊢ 𝐴 ∈ 𝐵 | |
| 2 | elex 3501 | . 2 ⊢ (𝐴 ∈ 𝐵 → 𝐴 ∈ V) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ V |
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