Definition df-he 42524

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 42523	. 2 wff 𝑅 hereditary 𝐴
4	2, 1	cima 5680	. . 3 class (𝑅 “ 𝐴)
5	4, 1	wss 3949	. 2 wff (𝑅 “ 𝐴) ⊆ 𝐴
6	3, 5	wb 205	1 wff (𝑅 hereditary 𝐴 ↔ (𝑅 “ 𝐴) ⊆ 𝐴)

This definition is referenced by:  dfhe2  42525  dfhe3  42526  heeq12  42527  sbcheg  42530  hess  42531  xphe  42532  0he  42533  he0  42535  unhe1  42536  snhesn  42537  dffrege76  42690