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| Mirrors > Home > MPE Home > Th. List > ne0d | Structured version Visualization version GIF version | ||
| Description: Deduction form of ne0i 4341. If a class has elements, then it is nonempty. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
| Ref | Expression |
|---|---|
| ne0d.1 | ⊢ (𝜑 → 𝐵 ∈ 𝐴) |
| Ref | Expression |
|---|---|
| ne0d | ⊢ (𝜑 → 𝐴 ≠ ∅) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ne0d.1 | . 2 ⊢ (𝜑 → 𝐵 ∈ 𝐴) | |
| 2 | ne0i 4341 | . 2 ⊢ (𝐵 ∈ 𝐴 → 𝐴 ≠ ∅) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ≠ ∅) |
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