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Mirrors > Home > MPE Home > Th. List > ne0d | Structured version Visualization version GIF version |
Description: Deduction form of ne0i 4233. 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 4233 | . 2 ⊢ (𝐵 ∈ 𝐴 → 𝐴 ≠ ∅) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ≠ ∅) |
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