Definition df-he 38907

Description: The property of relation 𝑅 being hereditary in class 𝐴. (Contributed by RP, 27-Mar-2020.)

Assertion

Ref	Expression
df-he	⊢ (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

Detailed syntax breakdown of Definition df-he

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cR	. . 3 class 𝑅
3	1, 2	whe 38906	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5345	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3798	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 198	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  38908  dfhe3  38909  heeq12  38910  sbcheg  38913  hess  38914  xphe  38915  0he  38916  he0  38918  unhe1  38919  snhesn  38920  dffrege76  39073