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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 4117. (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 4117 | . 2 ⊢ (𝐴 ∈ 𝒫 𝐵 → 𝐴 ⊆ 𝐵) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ⊆ 𝐵) |
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