Theorem 1sdom2ALT

Description: Alternate proof of 1sdom2 , shorter but requiring ax-un . (Contributed by NM, 4-Apr-2007) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	1sdom2ALT	⊢ 1o ≺ 2o

Proof

Step	Hyp	Ref	Expression
1		1onn	⊢ 1o ∈ ω
2		php4	⊢ ( 1o ∈ ω → 1o ≺ suc 1o )
3	1 2	ax-mp	⊢ 1o ≺ suc 1o
4		df-2o	⊢ 2o = suc 1o
5	3 4	breqtrri	⊢ 1o ≺ 2o