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Definition df-ptfin 26265
Description: Define "point-finite." (Contributed by Jeff Hankins, 21-Jan-2010.)
Assertion
Ref Expression
df-ptfin  |-  PtFin  =  {
x  |  A. y  e.  U. x { z  e.  x  |  y  e.  z }  e.  Fin }
Distinct variable group:    x, y, z

Detailed syntax breakdown of Definition df-ptfin
StepHypRef Expression
1 cptfin 26261 . 2  class  PtFin
2 vy . . . . . . 7  set  y
3 vz . . . . . . 7  set  z
42, 3wel 1685 . . . . . 6  wff  y  e.  z
5 vx . . . . . . 7  set  x
65cv 1622 . . . . . 6  class  x
74, 3, 6crab 2547 . . . . 5  class  { z  e.  x  |  y  e.  z }
8 cfn 6863 . . . . 5  class  Fin
97, 8wcel 1684 . . . 4  wff  { z  e.  x  |  y  e.  z }  e.  Fin
106cuni 3827 . . . 4  class  U. x
119, 2, 10wral 2543 . . 3  wff  A. y  e.  U. x { z  e.  x  |  y  e.  z }  e.  Fin
1211, 5cab 2269 . 2  class  { x  |  A. y  e.  U. x { z  e.  x  |  y  e.  z }  e.  Fin }
131, 12wceq 1623 1  wff  PtFin  =  {
x  |  A. y  e.  U. x { z  e.  x  |  y  e.  z }  e.  Fin }
Colors of variables: wff set class
This definition is referenced by:  isptfin  26295
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