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| Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.) | 
| Ref | Expression | 
|---|---|
| sseqtrdi.1 | ⊢ (𝜑 → 𝐴 ⊆ 𝐵) | 
| sseqtrdi.2 | ⊢ 𝐵 = 𝐶 | 
| Ref | Expression | 
|---|---|
| sseqtrdi | ⊢ (𝜑 → 𝐴 ⊆ 𝐶) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | sseqtrdi.1 | . 2 ⊢ (𝜑 → 𝐴 ⊆ 𝐵) | |
| 2 | sseqtrdi.2 | . . 3 ⊢ 𝐵 = 𝐶 | |
| 3 | 2 | sseq2i 4012 | . 2 ⊢ (𝐴 ⊆ 𝐵 ↔ 𝐴 ⊆ 𝐶) | 
| 4 | 1, 3 | sylib 218 | 1 ⊢ (𝜑 → 𝐴 ⊆ 𝐶) | 
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