Theorem bj-cnvcnv2

Description: The double converse of a class equals its restriction to the universe. (Contributed by NM, 8-Oct-2007) Do not depend on cnvcnv in order to prove it from cnvcnv2 . (Revised by BJ, 16-Oct-2026) Do not depend on cnvcnv . (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		cnvcnv3	$$⊢{A^{-1}}^{-1}=\left\{⟨x,y⟩|xAy\right\}$$
2		relpart	$$⊢{A\upharpoonright }_{\mathrm{V}}=\left\{⟨x,y⟩|xAy\right\}$$
3	1 2	eqtr4i	$$⊢{A^{-1}}^{-1}={A\upharpoonright }_{\mathrm{V}}$$