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| Mirrors > Home > MPE Home > Th. List > elexd | Structured version Visualization version GIF version | ||
| Description: If a class is a member of another class, then it is a set. Deduction associated with elex 3501. (Contributed by Glauco Siliprandi, 11-Oct-2020.) |
| Ref | Expression |
|---|---|
| elexd.1 | ⊢ (𝜑 → 𝐴 ∈ 𝑉) |
| Ref | Expression |
|---|---|
| elexd | ⊢ (𝜑 → 𝐴 ∈ V) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elexd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝑉) | |
| 2 | elex 3501 | . 2 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ V) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ∈ V) |
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