Theorem releqi

Description: Equality inference for the relation predicate. (Contributed by NM, 8-Dec-2006)

	Ref	Expression
Hypothesis	releqi.1	⊢ 𝐴 = 𝐵
Assertion	releqi	⊢ ( Rel 𝐴 ↔ Rel 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		releqi.1	⊢ 𝐴 = 𝐵
2		releq	⊢ ( 𝐴 = 𝐵 → ( Rel 𝐴 ↔ Rel 𝐵 ) )
3	1 2	ax-mp	⊢ ( Rel 𝐴 ↔ Rel 𝐵 )