Theorem eqbrtrrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 17-Sep-2004)

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

Proof

Step	Hyp	Ref	Expression
1		eqbrtrrid.1	⊢ 𝐵 = 𝐴
2		eqbrtrrid.2	⊢ ( 𝜑 → 𝐵 𝑅 𝐶 )
3		eqid	⊢ 𝐶 = 𝐶
4	2 1 3	3brtr3g	⊢ ( 𝜑 → 𝐴 𝑅 𝐶 )