Theorem releqd

Description: Equality deduction for the relation predicate. (Contributed by NM, 8-Mar-2014)

	Ref	Expression
Hypothesis	releqd.1	$$⊢\phi \to A=B$$
Assertion	releqd	$$⊢\phi \to \left(\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B\right)$$

Proof

Step	Hyp	Ref	Expression
1		releqd.1	$$⊢\phi \to A=B$$
2		releq	$$⊢A=B\to \left(\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B\right)$$
3	1 2	syl	$$⊢\phi \to \left(\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B\right)$$