Theorem 2onnALT

Description: Shorter proof of 2onn using Peano's postulates that depends on ax-un . (Contributed by NM, 28-Sep-2004) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	2onnALT	⊢ 2o ∈ ω

Proof

Step	Hyp	Ref	Expression
1		df-2o	⊢ 2o = suc 1o
2		1onn	⊢ 1o ∈ ω
3		peano2	⊢ ( 1o ∈ ω → suc 1o ∈ ω )
4	2 3	ax-mp	⊢ suc 1o ∈ ω
5	1 4	eqeltri	⊢ 2o ∈ ω