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| Mirrors > Home > MPE Home > Th. List > eqtr2d | Structured version Visualization version GIF version | ||
| Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999.) |
| Ref | Expression |
|---|---|
| eqtr2d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| eqtr2d.2 | ⊢ (𝜑 → 𝐵 = 𝐶) |
| Ref | Expression |
|---|---|
| eqtr2d | ⊢ (𝜑 → 𝐶 = 𝐴) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqtr2d.1 | . . 3 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | eqtr2d.2 | . . 3 ⊢ (𝜑 → 𝐵 = 𝐶) | |
| 3 | 1, 2 | eqtrd 2777 | . 2 ⊢ (𝜑 → 𝐴 = 𝐶) |
| 4 | 3 | eqcomd 2743 | 1 ⊢ (𝜑 → 𝐶 = 𝐴) |
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