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