Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-he Structured version   Visualization version   GIF version

Definition df-he 38902
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 38901 . 2 wff 𝑅 hereditary 𝐴
42, 1cima 5349 . . 3 class (𝑅𝐴)
54, 1wss 3798 . 2 wff (𝑅𝐴) ⊆ 𝐴
63, 5wb 198 1 wff (𝑅 hereditary 𝐴 ↔ (𝑅𝐴) ⊆ 𝐴)
Colors of variables: wff setvar class
This definition is referenced by:  dfhe2  38903  dfhe3  38904  heeq12  38905  sbcheg  38908  hess  38909  xphe  38910  0he  38911  he0  38913  unhe1  38914  snhesn  38915  dffrege76  39068
  Copyright terms: Public domain W3C validator