Theorem dfrel3

Description: Alternate definition of relation. (Contributed by NM, 14-May-2008)

	Ref	Expression
Assertion	dfrel3	$$⊢\mathrm{Rel}R\leftrightarrow {R\upharpoonright }_{\mathrm{V}}=R$$

Proof

Step	Hyp	Ref	Expression
1		dfrel2	$$⊢\mathrm{Rel}R\leftrightarrow {R^{-1}}^{-1}=R$$
2		cnvcnv2	$$⊢{R^{-1}}^{-1}={R\upharpoonright }_{\mathrm{V}}$$
3	2	eqeq1i	$$⊢{R^{-1}}^{-1}=R\leftrightarrow {R\upharpoonright }_{\mathrm{V}}=R$$
4	1 3	bitri	$$⊢\mathrm{Rel}R\leftrightarrow {R\upharpoonright }_{\mathrm{V}}=R$$