Metamath Proof Explorer

Theorem eqtr3

Description: A transitive law for class equality. (Contributed by NM, 20-May-2005) (Proof shortened by Wolf Lammen, 24-Oct-2024)

Ref Expression
Assertion eqtr3 ⊢ A = C ∧ B = C → A = B

Proof

Step Hyp Ref Expression
1 eqeq2 ⊢ B = C → A = B ↔ A = C
2 1 biimparc ⊢ A = C ∧ B = C → A = B