Definition df-he 43755

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 43754	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5634	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3911	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 206	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  43756  dfhe3  43757  heeq12  43758  sbcheg  43761  hess  43762  xphe  43763  0he  43764  he0  43766  unhe1  43767  snhesn  43768  dffrege76  43921