Definition df-he 45034

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 45033	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5661	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3900	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 209	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is used by:  dfhe2  45035  dfhe3  45036  heeq12  45037  sbcheg  45040  hess  45041  xphe  45042  0he  45043  he0  45045  unhe1  45046  snhesn  45047  dffrege76  45200