Metamath Proof Explorer


Theorem xpomen

Description: The Cartesian product of omega (the set of ordinal natural numbers) with itself is equinumerous to omega. Exercise 1 of Enderton p. 133. (Contributed by NM, 23-Jul-2004) (Revised by Mario Carneiro, 9-Mar-2013)

Ref Expression
Assertion xpomen
|- ( _om X. _om ) ~~ _om

Proof

Step Hyp Ref Expression
1 omelon
 |-  _om e. On
2 ssid
 |-  _om C_ _om
3 infxpen
 |-  ( ( _om e. On /\ _om C_ _om ) -> ( _om X. _om ) ~~ _om )
4 1 2 3 mp2an
 |-  ( _om X. _om ) ~~ _om