Definition df-he 44499

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 44498	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5664	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3905	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 209	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  44500  dfhe3  44501  heeq12  44502  sbcheg  44505  hess  44506  xphe  44507  0he  44508  he0  44510  unhe1  44511  snhesn  44512  dffrege76  44665