Description: Transitive law for class equality. Proposition 4.7(3) of TakeutiZaring p. 13. (Contributed by NM, 25-Jan-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | eqtr | ⊢ ( ( 𝐴 = 𝐵 ∧ 𝐵 = 𝐶 ) → 𝐴 = 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 | ⊢ ( 𝐴 = 𝐵 → ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐶 ) ) | |
2 | 1 | biimpar | ⊢ ( ( 𝐴 = 𝐵 ∧ 𝐵 = 𝐶 ) → 𝐴 = 𝐶 ) |