Theorem eqtr2

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

	Ref	Expression
Assertion	eqtr2	$$⊢\left(A=B\wedge A=C\right)\to B=C$$

Proof

Step	Hyp	Ref	Expression
1		eqcom	$$⊢A=B\leftrightarrow B=A$$
2		eqtr	$$⊢\left(B=A\wedge A=C\right)\to B=C$$
3	1 2	sylanb	$$⊢\left(A=B\wedge A=C\right)\to B=C$$