Metamath Proof Explorer

Definition df-fin6

Description: A set is VI-finite iff it behaves finitely under X. . Definition VI of Levy58 p. 4. (Contributed by Stefan O'Rear, 12-Nov-2014)

Ref Expression
Assertion df-fin6 
|- Fin6 = { x | ( x ~< 2o \/ x ~< ( x X. x ) ) }

Detailed syntax breakdown

Step Hyp Ref Expression
0 cfin6 
 |-  Fin6
1 vx 
 |-  x
2 1 cv 
 |-  x
3 csdm 
 |-  ~<
4 c2o 
 |-  2o
5 2 4 3 wbr 
 |-  x ~< 2o
6 2 2 cxp 
 |-  ( x X. x )
7 2 6 3 wbr 
 |-  x ~< ( x X. x )
8 5 7 wo 
 |-  ( x ~< 2o \/ x ~< ( x X. x ) )
9 8 1 cab 
 |-  { x | ( x ~< 2o \/ x ~< ( x X. x ) ) }
10 0 9 wceq 
 |-  Fin6 = { x | ( x ~< 2o \/ x ~< ( x X. x ) ) }