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Mirrors > Home > MPE Home > Th. List > eqtr4id | Structured version Visualization version GIF version |
Description: An equality transitivity deduction. (Contributed by NM, 29-Mar-1998.) |
Ref | Expression |
---|---|
eqtr4id.2 | ⊢ 𝐴 = 𝐵 |
eqtr4id.1 | ⊢ (𝜑 → 𝐶 = 𝐵) |
Ref | Expression |
---|---|
eqtr4id | ⊢ (𝜑 → 𝐴 = 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr4id.1 | . 2 ⊢ (𝜑 → 𝐶 = 𝐵) | |
2 | eqtr4id.2 | . . 3 ⊢ 𝐴 = 𝐵 | |
3 | 2 | eqcomi 2768 | . 2 ⊢ 𝐵 = 𝐴 |
4 | 1, 3 | eqtr2di 2811 | 1 ⊢ (𝜑 → 𝐴 = 𝐶) |
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