Users' Mathboxes Mathbox for Rodolfo Medina < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-prt Structured version   Unicode version

Definition df-prt 30444
Description: Define the partition predicate. (Contributed by Rodolfo Medina, 13-Oct-2010.)
Assertion
Ref Expression
df-prt  |-  ( Prt 
A  <->  A. x  e.  A  A. y  e.  A  ( x  =  y  \/  ( x  i^i  y
)  =  (/) ) )
Distinct variable group:    x, y, A

Detailed syntax breakdown of Definition df-prt
StepHypRef Expression
1 cA . . 3  class  A
21wprt 30443 . 2  wff  Prt  A
3 vx . . . . . 6  setvar  x
4 vy . . . . . 6  setvar  y
53, 4weq 1705 . . . . 5  wff  x  =  y
63cv 1378 . . . . . . 7  class  x
74cv 1378 . . . . . . 7  class  y
86, 7cin 3475 . . . . . 6  class  ( x  i^i  y )
9 c0 3785 . . . . . 6  class  (/)
108, 9wceq 1379 . . . . 5  wff  ( x  i^i  y )  =  (/)
115, 10wo 368 . . . 4  wff  ( x  =  y  \/  (
x  i^i  y )  =  (/) )
1211, 4, 1wral 2814 . . 3  wff  A. y  e.  A  ( x  =  y  \/  (
x  i^i  y )  =  (/) )
1312, 3, 1wral 2814 . 2  wff  A. x  e.  A  A. y  e.  A  ( x  =  y  \/  (
x  i^i  y )  =  (/) )
142, 13wb 184 1  wff  ( Prt 
A  <->  A. x  e.  A  A. y  e.  A  ( x  =  y  \/  ( x  i^i  y
)  =  (/) ) )
Colors of variables: wff setvar class
This definition is referenced by:  erprt  30445  prtlem14  30446
  Copyright terms: Public domain W3C validator