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Definition df-fin5 7799
Description: A set is V-finite iff it behaves finitely under  +c. Definition V of [Levy58] p. 3. (Contributed by Stefan O'Rear, 12-Nov-2014.)
Assertion
Ref Expression
df-fin5  |- FinV  =  {
x  |  ( x  =  (/)  \/  x  ~<  ( x  +c  x
) ) }

Detailed syntax breakdown of Definition df-fin5
StepHypRef Expression
1 cfin5 7792 . 2  class FinV
2 vx . . . . . 6  set  x
32cv 1618 . . . . 5  class  x
4 c0 3362 . . . . 5  class  (/)
53, 4wceq 1619 . . . 4  wff  x  =  (/)
6 ccda 7677 . . . . . 6  class  +c
73, 3, 6co 5710 . . . . 5  class  ( x  +c  x )
8 csdm 6748 . . . . 5  class  ~<
93, 7, 8wbr 3920 . . . 4  wff  x  ~<  ( x  +c  x )
105, 9wo 359 . . 3  wff  ( x  =  (/)  \/  x  ~<  ( x  +c  x
) )
1110, 2cab 2239 . 2  class  { x  |  ( x  =  (/)  \/  x  ~<  (
x  +c  x ) ) }
121, 11wceq 1619 1  wff FinV  =  {
x  |  ( x  =  (/)  \/  x  ~<  ( x  +c  x
) ) }
Colors of variables: wff set class
This definition is referenced by:  isfin5  7809
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