Definition df-he 37087

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 37086	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5041	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3540	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 195	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  37088  dfhe3  37089  heeq12  37090  sbcheg  37093  hess  37094  xphe  37095  0he  37096  he0  37098  unhe1  37099  snhesn  37100  dffrege76  37253