Theorem 3eqtr3i

Description: An inference from three chained equalities. (Contributed by NM, 6-May-1994) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr3i.1	|- A = B
	3eqtr3i.2	|- A = C
	3eqtr3i.3	|- B = D
Assertion	3eqtr3i	|- C = D

Proof

Step	Hyp	Ref	Expression
1		3eqtr3i.1	|- A = B
2		3eqtr3i.2	|- A = C
3		3eqtr3i.3	|- B = D
4	1 2	eqtr3i	|- B = C
5	4 3	eqtr3i	|- C = D