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