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| Description: An inference from three chained equalities. (Contributed by NM, 6-May-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) | 
| Ref | Expression | 
|---|---|
| 3eqtr3i.1 | ⊢ 𝐴 = 𝐵 | 
| 3eqtr3i.2 | ⊢ 𝐴 = 𝐶 | 
| 3eqtr3i.3 | ⊢ 𝐵 = 𝐷 | 
| Ref | Expression | 
|---|---|
| 3eqtr3i | ⊢ 𝐶 = 𝐷 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | 3eqtr3i.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
| 2 | 3eqtr3i.2 | . . 3 ⊢ 𝐴 = 𝐶 | |
| 3 | 1, 2 | eqtr3i 2766 | . 2 ⊢ 𝐵 = 𝐶 | 
| 4 | 3eqtr3i.3 | . 2 ⊢ 𝐵 = 𝐷 | |
| 5 | 3, 4 | eqtr3i 2766 | 1 ⊢ 𝐶 = 𝐷 | 
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