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 ∈ ω → suc 𝐴 ∈ ω )

Proof

Step	Hyp	Ref	Expression
1		peano2b	⊢ ( 𝐴 ∈ ω ↔ suc 𝐴 ∈ ω )
2	1	biimpi	⊢ ( 𝐴 ∈ ω → suc 𝐴 ∈ ω )