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| Mirrors > Home > MPE Home > Th. List > elpwid | Structured version Visualization version GIF version | ||
| Description: An element of a power class is a subclass. Deduction form of elpwi 4607. (Contributed by David Moews, 1-May-2017.) |
| Ref | Expression |
|---|---|
| elpwid.1 | ⊢ (𝜑 → 𝐴 ∈ 𝒫 𝐵) |
| Ref | Expression |
|---|---|
| elpwid | ⊢ (𝜑 → 𝐴 ⊆ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elpwid.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝒫 𝐵) | |
| 2 | elpwi 4607 | . 2 ⊢ (𝐴 ∈ 𝒫 𝐵 → 𝐴 ⊆ 𝐵) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ⊆ 𝐵) |
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