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Mirrors > Home > MPE Home > Th. List > breq1i | Structured version Visualization version GIF version |
Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
breq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
breq1i | ⊢ (𝐴𝑅𝐶 ↔ 𝐵𝑅𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | breq1 5030 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴𝑅𝐶 ↔ 𝐵𝑅𝐶)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴𝑅𝐶 ↔ 𝐵𝑅𝐶) |
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