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Mirrors > Home > MPE Home > Th. List > eqtr3id | Structured version Visualization version GIF version |
Description: An equality transitivity deduction. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqtr3id.1 | ⊢ 𝐵 = 𝐴 |
eqtr3id.2 | ⊢ (𝜑 → 𝐵 = 𝐶) |
Ref | Expression |
---|---|
eqtr3id | ⊢ (𝜑 → 𝐴 = 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr3id.1 | . . 3 ⊢ 𝐵 = 𝐴 | |
2 | 1 | eqcomi 2747 | . 2 ⊢ 𝐴 = 𝐵 |
3 | eqtr3id.2 | . 2 ⊢ (𝜑 → 𝐵 = 𝐶) | |
4 | 2, 3 | syl5eq 2785 | 1 ⊢ (𝜑 → 𝐴 = 𝐶) |
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