Theorem bj-tagss

Description: The tagging of a class is included in its powerclass. (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	bj-tagss	$$⊢tagA\subseteq 𝒫A$$

Proof

Step	Hyp	Ref	Expression
1		df-bj-tag	$$⊢tagA=snglA\cup \left\{\varnothing \right\}$$
2		bj-snglss	$$⊢snglA\subseteq 𝒫A$$
3		0elpw	$$⊢\varnothing \in 𝒫A$$
4		0ex	$$⊢\varnothing \in \mathrm{V}$$
5	4	snss	$$⊢\varnothing \in 𝒫A\leftrightarrow \left\{\varnothing \right\}\subseteq 𝒫A$$
6	3 5	mpbi	$$⊢\left\{\varnothing \right\}\subseteq 𝒫A$$
7	2 6	unssi	$$⊢snglA\cup \left\{\varnothing \right\}\subseteq 𝒫A$$
8	1 7	eqsstri	$$⊢tagA\subseteq 𝒫A$$