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Mirrors > Home > ILE Home > Th. List > eqtr4d | GIF version |
Description: An equality transitivity equality deduction. (Contributed by NM, 18-Jul-1995.) |
Ref | Expression |
---|---|
eqtr4d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
eqtr4d.2 | ⊢ (𝜑 → 𝐶 = 𝐵) |
Ref | Expression |
---|---|
eqtr4d | ⊢ (𝜑 → 𝐴 = 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr4d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
2 | eqtr4d.2 | . . 3 ⊢ (𝜑 → 𝐶 = 𝐵) | |
3 | 2 | eqcomd 2176 | . 2 ⊢ (𝜑 → 𝐵 = 𝐶) |
4 | 1, 3 | eqtrd 2203 | 1 ⊢ (𝜑 → 𝐴 = 𝐶) |
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