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| Mirrors > Home > MPE Home > Th. List > 3eqtr3g | Structured version Visualization version GIF version | ||
| Description: A chained equality inference, useful for converting from definitions. (Contributed by NM, 15-Nov-1994.) |
| Ref | Expression |
|---|---|
| 3eqtr3g.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| 3eqtr3g.2 | ⊢ 𝐴 = 𝐶 |
| 3eqtr3g.3 | ⊢ 𝐵 = 𝐷 |
| Ref | Expression |
|---|---|
| 3eqtr3g | ⊢ (𝜑 → 𝐶 = 𝐷) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3eqtr3g.2 | . . 3 ⊢ 𝐴 = 𝐶 | |
| 2 | 3eqtr3g.1 | . . 3 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 3 | 1, 2 | eqtr3id 2791 | . 2 ⊢ (𝜑 → 𝐶 = 𝐵) |
| 4 | 3eqtr3g.3 | . 2 ⊢ 𝐵 = 𝐷 | |
| 5 | 3, 4 | eqtrdi 2793 | 1 ⊢ (𝜑 → 𝐶 = 𝐷) |
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