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	$$⊢\left(A=B\wedge A=C\right)\to B=C$$

Proof

Step	Hyp	Ref	Expression
1		eqeq1	$$⊢A=B\to \left(A=C\leftrightarrow B=C\right)$$
2	1	biimpa	$$⊢\left(A=B\wedge A=C\right)\to B=C$$