Theorem 3eqtrri

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtri.1	|- A = B
	3eqtri.2	|- B = C
	3eqtri.3	|- C = D
Assertion	3eqtrri	|- D = A

Proof

Step	Hyp	Ref	Expression
1		3eqtri.1	|- A = B
2		3eqtri.2	|- B = C
3		3eqtri.3	|- C = D
4	1 2	eqtri	|- A = C
5	4 3	eqtr2i	|- D = A