Theorem idhe

Description: The identity relation is hereditary in any class. (Contributed by RP, 28-Mar-2020)

	Ref	Expression
Assertion	idhe	$$⊢\mathrm{I}hereditaryA$$

Proof

Step	Hyp	Ref	Expression
1		idssxp	$$⊢{\mathrm{I}\upharpoonright }_A\subseteq A\times A$$
2		dfhe2	$$⊢\mathrm{I}hereditaryA\leftrightarrow {\mathrm{I}\upharpoonright }_A\subseteq A\times A$$
3	1 2	mpbir	$$⊢\mathrm{I}hereditaryA$$