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Mirrors > Home > MPE Home > Th. List > sseqtrdi | Structured version Visualization version GIF version |
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 3947 | . 2 ⊢ (𝐴 ⊆ 𝐵 ↔ 𝐴 ⊆ 𝐶) |
4 | 1, 3 | sylib 221 | 1 ⊢ (𝜑 → 𝐴 ⊆ 𝐶) |
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