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| Mirrors > Home > MPE Home > Th. List > reseq1d | Structured version Visualization version GIF version | ||
| Description: Equality deduction for restrictions. (Contributed by NM, 21-Oct-2014.) |
| Ref | Expression |
|---|---|
| reseqd.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| reseq1d | ⊢ (𝜑 → (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | reseqd.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | reseq1 5991 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 ↾ 𝐶) = (𝐵 ↾ 𝐶)) |
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