Theorem eqtr2OLD

Description: Obsolete version of eqtr2 as of 24-Oct-2024. (Contributed by NM, 20-May-2005) (Proof shortened by Andrew Salmon, 25-May-2011) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	eqtr2OLD	$$⊢\left(A=B\wedge A=C\right)\to B=C$$

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