Theorem 3eqtr4i

Description: An inference from three chained equalities. (Contributed by NM, 26-May-1993) (Proof shortened by Andrew Salmon, 25-May-2011)

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

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	2 4	eqtr4i	⊢ 𝐶 = 𝐷