Theorem breq1i

Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996)

	Ref	Expression
Hypothesis	breq1i.1	⊢ 𝐴 = 𝐵
Assertion	breq1i	⊢ ( 𝐴 𝑅 𝐶 ↔ 𝐵 𝑅 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		breq1i.1	⊢ 𝐴 = 𝐵
2		breq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 𝑅 𝐶 ↔ 𝐵 𝑅 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 𝑅 𝐶 ↔ 𝐵 𝑅 𝐶 )