Definition df-he 38067

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 38066	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5117	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3574	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 196	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  38068  dfhe3  38069  heeq12  38070  sbcheg  38073  hess  38074  xphe  38075  0he  38076  he0  38078  unhe1  38079  snhesn  38080  dffrege76  38233