Definition df-he 43956

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 43955	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5625	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3899	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 206	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  43957  dfhe3  43958  heeq12  43959  sbcheg  43962  hess  43963  xphe  43964  0he  43965  he0  43967  unhe1  43968  snhesn  43969  dffrege76  44122