Theorem releq

Description: Equality theorem for the relation predicate. (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Assertion	releq	$$⊢A=B\to \left(\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B\right)$$

Proof

Step	Hyp	Ref	Expression
1		sseq1	$$⊢A=B\to \left(A\subseteq \mathrm{V}\times \mathrm{V}\leftrightarrow B\subseteq \mathrm{V}\times \mathrm{V}\right)$$
2		df-rel	$$⊢\mathrm{Rel}A\leftrightarrow A\subseteq \mathrm{V}\times \mathrm{V}$$
3		df-rel	$$⊢\mathrm{Rel}B\leftrightarrow B\subseteq \mathrm{V}\times \mathrm{V}$$
4	1 2 3	3bitr4g	$$⊢A=B\to \left(\mathrm{Rel}A\leftrightarrow \mathrm{Rel}B\right)$$