Theorem eqbrtrrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006)

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

Proof

Step	Hyp	Ref	Expression
1		eqbrtrrdi.1	⊢ ( 𝜑 → 𝐵 = 𝐴 )
2		eqbrtrrdi.2	⊢ 𝐵 𝑅 𝐶
3	1	eqcomd	⊢ ( 𝜑 → 𝐴 = 𝐵 )
4	3 2	eqbrtrdi	⊢ ( 𝜑 → 𝐴 𝑅 𝐶 )