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 e. _om -> suc A e. _om )

Proof

Step	Hyp	Ref	Expression
1		peano2b	|- ( A e. _om <-> suc A e. _om )
2	1	biimpi	|- ( A e. _om -> suc A e. _om )