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 ω ≈ suc ω

Proof

Step Hyp Ref Expression
1 omex ω ∈ V
2 limom Lim ω
3 2 limensuci ( ω ∈ V → ω ≈ suc ω )
4 1 3 ax-mp ω ≈ suc ω