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	$$⊢A\in \mathrm{\omega }\to \mathrm{suc}A\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		nsuceq0	$$⊢\mathrm{suc}A\ne \varnothing$$
2	1	a1i	$$⊢A\in \mathrm{\omega }\to \mathrm{suc}A\ne \varnothing$$