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Definition df-he 43038
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 43037 . 2 wff 𝑅 hereditary 𝐴
42, 1cima 5670 . . 3 class (𝑅𝐴)
54, 1wss 3941 . 2 wff (𝑅𝐴) ⊆ 𝐴
63, 5wb 205 1 wff (𝑅 hereditary 𝐴 ↔ (𝑅𝐴) ⊆ 𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dfhe2  43039  dfhe3  43040  heeq12  43041  sbcheg  43044  hess  43045  xphe  43046  0he  43047  he0  43049  unhe1  43050  snhesn  43051  dffrege76  43204
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