Theorem breqtrri

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

	Ref	Expression
Hypotheses	breqtrr.1	⊢ 𝐴 𝑅 𝐵
	breqtrr.2	⊢ 𝐶 = 𝐵
Assertion	breqtrri	⊢ 𝐴 𝑅 𝐶

Proof

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