Theorem 3eqtr2ri

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

	Ref	Expression
Hypotheses	3eqtr2i.1	⊢ 𝐴 = 𝐵
	3eqtr2i.2	⊢ 𝐶 = 𝐵
	3eqtr2i.3	⊢ 𝐶 = 𝐷
Assertion	3eqtr2ri	⊢ 𝐷 = 𝐴

Proof

Step	Hyp	Ref	Expression
1		3eqtr2i.1	⊢ 𝐴 = 𝐵
2		3eqtr2i.2	⊢ 𝐶 = 𝐵
3		3eqtr2i.3	⊢ 𝐶 = 𝐷
4	1 2	eqtr4i	⊢ 𝐴 = 𝐶
5	4 3	eqtr2i	⊢ 𝐷 = 𝐴