Theorem peano3

Description: The successor of any natural number is not zero. One of Peano's five postulates for arithmetic. Proposition 7.30(3) of TakeutiZaring p. 42. (Contributed by NM, 3-Sep-2003)

	Ref	Expression
Assertion	peano3	⊢ ( 𝐴 ∈ ω → suc 𝐴 ≠ ∅ )

Proof

Step	Hyp	Ref	Expression
1		nsuceq0	⊢ suc 𝐴 ≠ ∅
2	1	a1i	⊢ ( 𝐴 ∈ ω → suc 𝐴 ≠ ∅ )