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| Mirrors > Home > MPE Home > Th. List > breqtrrdi | Structured version Visualization version GIF version | ||
| Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005.) |
| Ref | Expression |
|---|---|
| breqtrrdi.1 | ⊢ (𝜑 → 𝐴𝑅𝐵) |
| breqtrrdi.2 | ⊢ 𝐶 = 𝐵 |
| Ref | Expression |
|---|---|
| breqtrrdi | ⊢ (𝜑 → 𝐴𝑅𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | breqtrrdi.1 | . 2 ⊢ (𝜑 → 𝐴𝑅𝐵) | |
| 2 | breqtrrdi.2 | . . 3 ⊢ 𝐶 = 𝐵 | |
| 3 | 2 | eqcomi 2746 | . 2 ⊢ 𝐵 = 𝐶 |
| 4 | 1, 3 | breqtrdi 5184 | 1 ⊢ (𝜑 → 𝐴𝑅𝐶) |
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