Theorem eqbrtrri

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

	Ref	Expression
Hypotheses	eqbrtrr.1	⊢ 𝐴 = 𝐵
	eqbrtrr.2	⊢ 𝐴 𝑅 𝐶
Assertion	eqbrtrri	⊢ 𝐵 𝑅 𝐶

Proof

Step	Hyp	Ref	Expression
1		eqbrtrr.1	⊢ 𝐴 = 𝐵
2		eqbrtrr.2	⊢ 𝐴 𝑅 𝐶
3	1	eqcomi	⊢ 𝐵 = 𝐴
4	3 2	eqbrtri	⊢ 𝐵 𝑅 𝐶