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| Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.) | 
| Ref | Expression | 
|---|---|
| breq1i.1 | ⊢ 𝐴 = 𝐵 | 
| Ref | Expression | 
|---|---|
| breq2i | ⊢ (𝐶𝑅𝐴 ↔ 𝐶𝑅𝐵) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | breq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 2 | breq2 5146 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶𝑅𝐴 ↔ 𝐶𝑅𝐵)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐶𝑅𝐴 ↔ 𝐶𝑅𝐵) | 
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