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| Mirrors > Home > MPE Home > Th. List > 3eqtri | Structured version Visualization version GIF version | ||
| Description: An inference from three chained equalities. (Contributed by NM, 29-Aug-1993.) |
| Ref | Expression |
|---|---|
| 3eqtri.1 | ⊢ 𝐴 = 𝐵 |
| 3eqtri.2 | ⊢ 𝐵 = 𝐶 |
| 3eqtri.3 | ⊢ 𝐶 = 𝐷 |
| Ref | Expression |
|---|---|
| 3eqtri | ⊢ 𝐴 = 𝐷 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3eqtri.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 2 | 3eqtri.2 | . . 3 ⊢ 𝐵 = 𝐶 | |
| 3 | 3eqtri.3 | . . 3 ⊢ 𝐶 = 𝐷 | |
| 4 | 2, 3 | eqtri 2765 | . 2 ⊢ 𝐵 = 𝐷 |
| 5 | 1, 4 | eqtri 2765 | 1 ⊢ 𝐴 = 𝐷 |
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