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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 2779 | . 2 ⊢ (𝜑 → 𝐴 = 𝐶) |
4 | 3 | eqcomd 2745 | 1 ⊢ (𝜑 → 𝐶 = 𝐴) |
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