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Mirrors > Home > ILE Home > Th. List > eqtri | GIF version |
Description: An equality transitivity inference. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqtri.1 | ⊢ 𝐴 = 𝐵 |
eqtri.2 | ⊢ 𝐵 = 𝐶 |
Ref | Expression |
---|---|
eqtri | ⊢ 𝐴 = 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtri.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | eqtri.2 | . . 3 ⊢ 𝐵 = 𝐶 | |
3 | 2 | eqeq2i 2148 | . 2 ⊢ (𝐴 = 𝐵 ↔ 𝐴 = 𝐶) |
4 | 1, 3 | mpbi 144 | 1 ⊢ 𝐴 = 𝐶 |
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