Theorem sshepw

Description: The relation between sets and their subsets is hereditary in the powerclass of any class. (Contributed by RP, 28-Mar-2020)

	Ref	Expression
Assertion	sshepw	$$⊢\left({[\subset ]}^{-1}\cup \mathrm{I}\right)hereditary𝒫A$$

Proof

Step	Hyp	Ref	Expression
1		psshepw	$$⊢{[\subset ]}^{-1}hereditary𝒫A$$
2		idhe	$$⊢\mathrm{I}hereditary𝒫A$$
3		unhe1	$$⊢\left({[\subset ]}^{-1}hereditary𝒫A\wedge \mathrm{I}hereditary𝒫A\right)\to \left({[\subset ]}^{-1}\cup \mathrm{I}\right)hereditary𝒫A$$
4	1 2 3	mp2an	$$⊢\left({[\subset ]}^{-1}\cup \mathrm{I}\right)hereditary𝒫A$$