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| Mirrors > Home > MPE Home > Th. List > breq1d | Structured version Visualization version GIF version | ||
| Description: Equality deduction for a binary relation. (Contributed by NM, 8-Feb-1996.) |
| Ref | Expression |
|---|---|
| breq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| breq1d | ⊢ (𝜑 → (𝐴𝑅𝐶 ↔ 𝐵𝑅𝐶)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | breq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | breq1 5146 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴𝑅𝐶 ↔ 𝐵𝑅𝐶)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴𝑅𝐶 ↔ 𝐵𝑅𝐶)) |
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