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Mirrors > Home > MPE Home > Th. List > syl5eqbr | Structured version Visualization version GIF version |
Description: A chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999.) |
Ref | Expression |
---|---|
syl5eqbr.1 | ⊢ 𝐴 = 𝐵 |
syl5eqbr.2 | ⊢ (𝜑 → 𝐵𝑅𝐶) |
Ref | Expression |
---|---|
syl5eqbr | ⊢ (𝜑 → 𝐴𝑅𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl5eqbr.2 | . 2 ⊢ (𝜑 → 𝐵𝑅𝐶) | |
2 | syl5eqbr.1 | . 2 ⊢ 𝐴 = 𝐵 | |
3 | eqid 2610 | . 2 ⊢ 𝐶 = 𝐶 | |
4 | 1, 2, 3 | 3brtr4g 4617 | 1 ⊢ (𝜑 → 𝐴𝑅𝐶) |
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