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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 2047 | . 2 ⊢ (A = B ↔ A = 𝐶) |
4 | 1, 3 | mpbi 133 | 1 ⊢ A = 𝐶 |
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