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 ω × ω ω

Proof

Step Hyp Ref Expression
1 omelon ω On
2 ssid ω ω
3 infxpen ω On ω ω ω × ω ω
4 1 2 3 mp2an ω × ω ω