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Definition df-prt 26843
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 26842 . 2  wff  Prt  A
3 vx . . . . . 6  set  x
4 vy . . . . . 6  set  y
53, 4weq 1633 . . . . 5  wff  x  =  y
63cv 1631 . . . . . . 7  class  x
74cv 1631 . . . . . . 7  class  y
86, 7cin 3164 . . . . . 6  class  ( x  i^i  y )
9 c0 3468 . . . . . 6  class  (/)
108, 9wceq 1632 . . . . 5  wff  ( x  i^i  y )  =  (/)
115, 10wo 357 . . . 4  wff  ( x  =  y  \/  (
x  i^i  y )  =  (/) )
1211, 4, 1wral 2556 . . 3  wff  A. y  e.  A  ( x  =  y  \/  (
x  i^i  y )  =  (/) )
1312, 3, 1wral 2556 . 2  wff  A. x  e.  A  A. y  e.  A  ( x  =  y  \/  (
x  i^i  y )  =  (/) )
142, 13wb 176 1  wff  ( Prt 
A  <->  A. x  e.  A  A. y  e.  A  ( x  =  y  \/  ( x  i^i  y
)  =  (/) ) )
Colors of variables: wff set class
This definition is referenced by:  erprt  26844  prtlem14  26845
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