Theorem breqtri

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

	Ref	Expression
Hypotheses	breqtr.1	⊢ 𝐴 𝑅 𝐵
	breqtr.2	⊢ 𝐵 = 𝐶
Assertion	breqtri	⊢ 𝐴 𝑅 𝐶

Proof

Step	Hyp	Ref	Expression
1		breqtr.1	⊢ 𝐴 𝑅 𝐵
2		breqtr.2	⊢ 𝐵 = 𝐶
3	2	breq2i	⊢ ( 𝐴 𝑅 𝐵 ↔ 𝐴 𝑅 𝐶 )
4	1 3	mpbi	⊢ 𝐴 𝑅 𝐶