Definition df-he 44200

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 44199	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5634	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3889	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 206	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  44201  dfhe3  44202  heeq12  44203  sbcheg  44206  hess  44207  xphe  44208  0he  44209  he0  44211  unhe1  44212  snhesn  44213  dffrege76  44366