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| Mirrors > Home > MPE Home > Th. List > eqtri | Structured version Visualization version GIF version | ||
| Description: An equality transitivity inference. (Contributed by NM, 26-May-1993.) |
| Ref | Expression |
|---|---|
| eqtri.1 | ⊢ 𝐴 = 𝐵 |
| eqtri.2 | ⊢ 𝐵 = 𝐶 |
| Ref | Expression |
|---|---|
| eqtri | ⊢ 𝐴 = 𝐶 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqtri.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 2 | eqtri.2 | . . 3 ⊢ 𝐵 = 𝐶 | |
| 3 | 2 | eqeq2i 2750 | . 2 ⊢ (𝐴 = 𝐵 ↔ 𝐴 = 𝐶) |
| 4 | 1, 3 | mpbi 230 | 1 ⊢ 𝐴 = 𝐶 |
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