Definition df-he 43763

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 43762	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5692	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3963	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 206	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  43764  dfhe3  43765  heeq12  43766  sbcheg  43769  hess  43770  xphe  43771  0he  43772  he0  43774  unhe1  43775  snhesn  43776  dffrege76  43929