Definition df-he 40126

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 40125	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5560	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3938	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 208	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  40127  dfhe3  40128  heeq12  40129  sbcheg  40132  hess  40133  xphe  40134  0he  40135  he0  40137  unhe1  40138  snhesn  40139  dffrege76  40292