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