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| Description: A chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999.) | 
| Ref | Expression | 
|---|---|
| eqbrtrid.1 | ⊢ 𝐴 = 𝐵 | 
| eqbrtrid.2 | ⊢ (𝜑 → 𝐵𝑅𝐶) | 
| Ref | Expression | 
|---|---|
| eqbrtrid | ⊢ (𝜑 → 𝐴𝑅𝐶) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | eqbrtrid.2 | . 2 ⊢ (𝜑 → 𝐵𝑅𝐶) | |
| 2 | eqbrtrid.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 3 | eqid 2736 | . 2 ⊢ 𝐶 = 𝐶 | |
| 4 | 1, 2, 3 | 3brtr4g 5176 | 1 ⊢ (𝜑 → 𝐴𝑅𝐶) | 
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