Theorem 3eqtr4ri

Description: An inference from three chained equalities. (Contributed by NM, 2-Sep-1995) (Proof shortened by Andrew Salmon, 25-May-2011)

	Ref	Expression
Hypotheses	3eqtr4i.1	⊢ 𝐴 = 𝐵
	3eqtr4i.2	⊢ 𝐶 = 𝐴
	3eqtr4i.3	⊢ 𝐷 = 𝐵
Assertion	3eqtr4ri	⊢ 𝐷 = 𝐶

Proof

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