Theorem eqtr2

Description: A transitive law for class equality. (Contributed by NM, 20-May-2005) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 24-Oct-2024)

	Ref	Expression
Assertion	eqtr2	|- ( ( A = B /\ A = C ) -> B = C )

Proof

Step	Hyp	Ref	Expression
1		eqeq1	|- ( A = B -> ( A = C <-> B = C ) )
2	1	biimpa	|- ( ( A = B /\ A = C ) -> B = C )