Metamath Proof Explorer

Theorem omensuc

Description: The set of natural numbers is equinumerous to its successor. (Contributed by NM, 30-Oct-2003)

Ref Expression
Assertion omensuc 
|- _om ~~ suc _om

Proof

Step Hyp Ref Expression
1 omex 
 |-  _om e. _V
2 limom 
 |-  Lim _om
3 2 limensuci 
 |-  ( _om e. _V -> _om ~~ suc _om )
4 1 3 ax-mp 
 |-  _om ~~ suc _om