Theorem eqtr3

Description: A transitive law for class equality. (Contributed by NM, 20-May-2005)

	Ref	Expression
Assertion	eqtr3	$$⊢\left(A=C\wedge B=C\right)\to A=B$$

Proof

Step	Hyp	Ref	Expression
1		eqcom	$$⊢B=C\leftrightarrow C=B$$
2		eqtr	$$⊢\left(A=C\wedge C=B\right)\to A=B$$
3	1 2	sylan2b	$$⊢\left(A=C\wedge B=C\right)\to A=B$$