Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  df-dcin Unicode version

Definition df-dcin 11124
Description: Define decidability of a class in another. (Contributed by BJ, 19-Feb-2022.)
Assertion
Ref Expression
df-dcin  |-  ( A DECIDin  B  <->  A. x  e.  B DECID  x  e.  A
)
Distinct variable groups:    x, A    x, B

Detailed syntax breakdown of Definition df-dcin
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
31, 2wdcin 11123 . 2  wff  A DECIDin  B
4 vx . . . . . 6  setvar  x
54cv 1286 . . . . 5  class  x
65, 1wcel 1436 . . . 4  wff  x  e.  A
76wdc 778 . . 3  wff DECID  x  e.  A
87, 4, 2wral 2355 . 2  wff  A. x  e.  B DECID  x  e.  A
93, 8wb 103 1  wff  ( A DECIDin  B  <->  A. x  e.  B DECID  x  e.  A
)
Colors of variables: wff set class
This definition is referenced by:  decidi  11125  decidr  11126  sumdc2  11129
  Copyright terms: Public domain W3C validator