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| Mirrors > Home > MPE Home > Th. List > sseq2d | Structured version Visualization version GIF version | ||
| Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994.) |
| Ref | Expression |
|---|---|
| sseq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| sseq2d | ⊢ (𝜑 → (𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sseq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | sseq2 4010 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵)) |
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