Theorem breqtrrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005)

	Ref	Expression
Hypotheses	breqtrrdi.1	⊢ ( 𝜑 → 𝐴 𝑅 𝐵 )
	breqtrrdi.2	⊢ 𝐶 = 𝐵
Assertion	breqtrrdi	⊢ ( 𝜑 → 𝐴 𝑅 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		breqtrrdi.1	⊢ ( 𝜑 → 𝐴 𝑅 𝐵 )
2		breqtrrdi.2	⊢ 𝐶 = 𝐵
3	2	eqcomi	⊢ 𝐵 = 𝐶
4	1 3	breqtrdi	⊢ ( 𝜑 → 𝐴 𝑅 𝐶 )