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Mirrors > Home > MPE Home > Th. List > eqbrtrrid | Structured version Visualization version GIF version |
Description: A chained equality inference for a binary relation. (Contributed by NM, 17-Sep-2004.) |
Ref | Expression |
---|---|
eqbrtrrid.1 | ⊢ 𝐵 = 𝐴 |
eqbrtrrid.2 | ⊢ (𝜑 → 𝐵𝑅𝐶) |
Ref | Expression |
---|---|
eqbrtrrid | ⊢ (𝜑 → 𝐴𝑅𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrrid.2 | . 2 ⊢ (𝜑 → 𝐵𝑅𝐶) | |
2 | eqbrtrrid.1 | . 2 ⊢ 𝐵 = 𝐴 | |
3 | eqid 2738 | . 2 ⊢ 𝐶 = 𝐶 | |
4 | 1, 2, 3 | 3brtr3g 5063 | 1 ⊢ (𝜑 → 𝐴𝑅𝐶) |
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