Theorem 3eqtri

Description: An inference from three chained equalities. (Contributed by NM, 29-Aug-1993)

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

Proof

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