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