Theorem cnvcnvss

Description: The double converse of a class is a subclass. Exercise 2 of TakeutiZaring p. 25. (Contributed by NM, 23-Jul-2004)

	Ref	Expression
Assertion	cnvcnvss	$$⊢{A^{-1}}^{-1}\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		cnvcnv	$$⊢{A^{-1}}^{-1}=A\cap \left(\mathrm{V}\times \mathrm{V}\right)$$
2		inss1	$$⊢A\cap \left(\mathrm{V}\times \mathrm{V}\right)\subseteq A$$
3	1 2	eqsstri	$$⊢{A^{-1}}^{-1}\subseteq A$$