Description: A transitive law for class equality. (Contributed by NM, 20-May-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | eqtr3 | ⊢ ( ( 𝐴 = 𝐶 ∧ 𝐵 = 𝐶 ) → 𝐴 = 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom | ⊢ ( 𝐵 = 𝐶 ↔ 𝐶 = 𝐵 ) | |
2 | eqtr | ⊢ ( ( 𝐴 = 𝐶 ∧ 𝐶 = 𝐵 ) → 𝐴 = 𝐵 ) | |
3 | 1 2 | sylan2b | ⊢ ( ( 𝐴 = 𝐶 ∧ 𝐵 = 𝐶 ) → 𝐴 = 𝐵 ) |