MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-fin7 Unicode version

Definition df-fin7 8692
Description: A set is VII-finite iff it cannot be infinitely well-ordered. Equivalent to definition VII of [Levy58] p. 4. (Contributed by Stefan O'Rear, 12-Nov-2014.)
Assertion
Ref Expression
df-fin7
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-fin7
StepHypRef Expression
1 cfin7 8685 . 2
2 vx . . . . . . 7
32cv 1394 . . . . . 6
4 vy . . . . . . 7
54cv 1394 . . . . . 6
6 cen 7533 . . . . . 6
73, 5, 6wbr 4452 . . . . 5
8 con0 4883 . . . . . 6
9 com 6700 . . . . . 6
108, 9cdif 3472 . . . . 5
117, 4, 10wrex 2808 . . . 4
1211wn 3 . . 3
1312, 2cab 2442 . 2
141, 13wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  isfin7  8702
  Copyright terms: Public domain W3C validator