Definition df-he 42514

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 42513	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5679	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3948	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 205	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  42515  dfhe3  42516  heeq12  42517  sbcheg  42520  hess  42521  xphe  42522  0he  42523  he0  42525  unhe1  42526  snhesn  42527  dffrege76  42680