Theorem 3brtr4i

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999)

	Ref	Expression
Hypotheses	3brtr4.1	⊢ 𝐴 𝑅 𝐵
	3brtr4.2	⊢ 𝐶 = 𝐴
	3brtr4.3	⊢ 𝐷 = 𝐵
Assertion	3brtr4i	⊢ 𝐶 𝑅 𝐷

Proof

Step	Hyp	Ref	Expression
1		3brtr4.1	⊢ 𝐴 𝑅 𝐵
2		3brtr4.2	⊢ 𝐶 = 𝐴
3		3brtr4.3	⊢ 𝐷 = 𝐵
4	2 1	eqbrtri	⊢ 𝐶 𝑅 𝐵
5	4 3	breqtrri	⊢ 𝐶 𝑅 𝐷