Theorem peano2b

Description: A class belongs to omega iff its successor does. (Contributed by NM, 3-Dec-1995)

	Ref	Expression
Assertion	peano2b	⊢ ( 𝐴 ∈ ω ↔ suc 𝐴 ∈ ω )

Proof

Step	Hyp	Ref	Expression
1		limom	⊢ Lim ω
2		limsuc	⊢ ( Lim ω → ( 𝐴 ∈ ω ↔ suc 𝐴 ∈ ω ) )
3	1 2	ax-mp	⊢ ( 𝐴 ∈ ω ↔ suc 𝐴 ∈ ω )