Theorem idhe

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

	Ref	Expression
Assertion	idhe	⊢ I hereditary 𝐴

Proof

Step	Hyp	Ref	Expression
1		idssxp	⊢ ( I ↾ 𝐴 ) ⊆ ( 𝐴 × 𝐴 )
2		dfhe2	⊢ ( I hereditary 𝐴 ↔ ( I ↾ 𝐴 ) ⊆ ( 𝐴 × 𝐴 ) )
3	1 2	mpbir	⊢ I hereditary 𝐴