Theorem releqi

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

	Ref	Expression
Hypothesis	releqi.1	$$⊢A=B$$
Assertion	releqi	$$⊢\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B$$

Proof

Step	Hyp	Ref	Expression
1		releqi.1	$$⊢A=B$$
2		releq	$$⊢A=B\to \left(\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B\right)$$
3	1 2	ax-mp	$$⊢\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B$$