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| Mirrors > Home > MPE Home > Th. List > sstri | Structured version Visualization version GIF version | ||
| Description: Subclass transitivity inference. (Contributed by NM, 5-May-2000.) |
| Ref | Expression |
|---|---|
| sstri.1 | ⊢ 𝐴 ⊆ 𝐵 |
| sstri.2 | ⊢ 𝐵 ⊆ 𝐶 |
| Ref | Expression |
|---|---|
| sstri | ⊢ 𝐴 ⊆ 𝐶 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sstri.1 | . 2 ⊢ 𝐴 ⊆ 𝐵 | |
| 2 | sstri.2 | . 2 ⊢ 𝐵 ⊆ 𝐶 | |
| 3 | sstr2 3990 | . 2 ⊢ (𝐴 ⊆ 𝐵 → (𝐵 ⊆ 𝐶 → 𝐴 ⊆ 𝐶)) | |
| 4 | 1, 2, 3 | mp2 9 | 1 ⊢ 𝐴 ⊆ 𝐶 |
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