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Definition df-he 40328
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 ↔ (𝑅𝐴) ⊆ 𝐴)

Detailed syntax breakdown of Definition df-he
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cR . . 3 class 𝑅
31, 2whe 40327 . 2 wff 𝑅 hereditary 𝐴
42, 1cima 5545 . . 3 class (𝑅𝐴)
54, 1wss 3919 . 2 wff (𝑅𝐴) ⊆ 𝐴
63, 5wb 209 1 wff (𝑅 hereditary 𝐴 ↔ (𝑅𝐴) ⊆ 𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dfhe2  40329  dfhe3  40330  heeq12  40331  sbcheg  40334  hess  40335  xphe  40336  0he  40337  he0  40339  unhe1  40340  snhesn  40341  dffrege76  40494
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