Theorem brcnvssrid

Description: Any set is a converse subset of itself. (Contributed by Peter Mazsa, 9-Jun-2021)

	Ref	Expression
Assertion	brcnvssrid	$$⊢A\in V\to A{\mathrm{S}}^{-1}A$$

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢A\subseteq A$$
2		brcnvssr	$$⊢A\in V\to \left(A{\mathrm{S}}^{-1}A\leftrightarrow A\subseteq A\right)$$
3	1 2	mpbiri	$$⊢A\in V\to A{\mathrm{S}}^{-1}A$$