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| Mirrors > Home > MPE Home > Th. List > elpwi | Structured version Visualization version GIF version | ||
| Description: Subset relation implied by membership in a power class. (Contributed by NM, 17-Feb-2007.) |
| Ref | Expression |
|---|---|
| elpwi | ⊢ (𝐴 ∈ 𝒫 𝐵 → 𝐴 ⊆ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elpwg 4603 | . 2 ⊢ (𝐴 ∈ 𝒫 𝐵 → (𝐴 ∈ 𝒫 𝐵 ↔ 𝐴 ⊆ 𝐵)) | |
| 2 | 1 | ibi 267 | 1 ⊢ (𝐴 ∈ 𝒫 𝐵 → 𝐴 ⊆ 𝐵) |
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