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Metamath Proof Explorer

Theorem peano2

Description: The successor of any natural number is a natural number. One of Peano's five postulates for arithmetic. Proposition 7.30(2) of TakeutiZaring p. 42. (Contributed by NM, 3-Sep-2003)

		Ref	Expression
	Assertion	peano2	$⊢ A \in ω \to suc A \in ω$

Proof

Step	Hyp	Ref	Expression
1		peano2b	$⊢ A \in ω \leftrightarrow suc A \in ω$
2	1	biimpi	$⊢ A \in ω \to suc A \in ω$