Theorem eqbrtri

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999)

	Ref	Expression
Hypotheses	eqbrtr.1	⊢ 𝐴 = 𝐵
	eqbrtr.2	⊢ 𝐵 𝑅 𝐶
Assertion	eqbrtri	⊢ 𝐴 𝑅 𝐶

Proof

Step	Hyp	Ref	Expression
1		eqbrtr.1	⊢ 𝐴 = 𝐵
2		eqbrtr.2	⊢ 𝐵 𝑅 𝐶
3	1	breq1i	⊢ ( 𝐴 𝑅 𝐶 ↔ 𝐵 𝑅 𝐶 )
4	2 3	mpbir	⊢ 𝐴 𝑅 𝐶