Definition df-he 43746

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 43745	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5622	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3903	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 206	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  43747  dfhe3  43748  heeq12  43749  sbcheg  43752  hess  43753  xphe  43754  0he  43755  he0  43757  unhe1  43758  snhesn  43759  dffrege76  43912