| Mathbox for Norm Megill |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > hllatd | Structured version Visualization version GIF version | ||
| Description: Deduction form of hllat 39364. A Hilbert lattice is a lattice. (Contributed by BJ, 14-Aug-2022.) |
| Ref | Expression |
|---|---|
| hllatd.1 | ⊢ (𝜑 → 𝐾 ∈ HL) |
| Ref | Expression |
|---|---|
| hllatd | ⊢ (𝜑 → 𝐾 ∈ Lat) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hllatd.1 | . 2 ⊢ (𝜑 → 𝐾 ∈ HL) | |
| 2 | hllat 39364 | . 2 ⊢ (𝐾 ∈ HL → 𝐾 ∈ Lat) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐾 ∈ Lat) |
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