Definition df-he 44557

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 44556	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5666	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3906	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 209	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is used by:  dfhe2  44558  dfhe3  44559  heeq12  44560  sbcheg  44563  hess  44564  xphe  44565  0he  44566  he0  44568  unhe1  44569  snhesn  44570  dffrege76  44723