Theorem cnvcnv2

Description: The double converse of a class equals its restriction to the universe. (Contributed by NM, 8-Oct-2007)

	Ref	Expression
Assertion	cnvcnv2	$$⊢{A^{-1}}^{-1}={A\upharpoonright }_{\mathrm{V}}$$

Proof

Step	Hyp	Ref	Expression
1		cnvcnv	$$⊢{A^{-1}}^{-1}=A\cap \left(\mathrm{V}\times \mathrm{V}\right)$$
2		df-res	$$⊢{A\upharpoonright }_{\mathrm{V}}=A\cap \left(\mathrm{V}\times \mathrm{V}\right)$$
3	1 2	eqtr4i	$$⊢{A^{-1}}^{-1}={A\upharpoonright }_{\mathrm{V}}$$