Theorem eqtri

Description: An equality transitivity inference. (Contributed by NM, 26-May-1993)

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

Proof

Step	Hyp	Ref	Expression
1		eqtri.1	⊢ 𝐴 = 𝐵
2		eqtri.2	⊢ 𝐵 = 𝐶
3	2	eqeq2i	⊢ ( 𝐴 = 𝐵 ↔ 𝐴 = 𝐶 )
4	1 3	mpbi	⊢ 𝐴 = 𝐶