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Metamath Proof Explorer

Theorem peano2b

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

		Ref	Expression
	Assertion	peano2b	$⊢ A \in ω \leftrightarrow suc A \in ω$

Step	Hyp	Ref	Expression
1		limom	$⊢ Lim ω$
2		limsuc	$⊢ Lim ω \to (A \in ω \leftrightarrow suc A \in ω)$
3	1 2	ax-mp	$⊢ A \in ω \leftrightarrow suc A \in ω$