Theorem eqbrtrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999)

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

Proof

Step	Hyp	Ref	Expression
1		eqbrtrid.1	⊢ 𝐴 = 𝐵
2		eqbrtrid.2	⊢ ( 𝜑 → 𝐵 𝑅 𝐶 )
3		eqid	⊢ 𝐶 = 𝐶
4	2 1 3	3brtr4g	⊢ ( 𝜑 → 𝐴 𝑅 𝐶 )