Theorem ord3

Description: Ordinal 3 is an ordinal class. (Contributed by BTernaryTau, 6-Jan-2025)

	Ref	Expression
Assertion	ord3	⊢ Ord 3o

Proof

Step	Hyp	Ref	Expression
1		2on	⊢ 2o ∈ On
2		eloni	⊢ ( 2o ∈ On → Ord 2o )
3		ordsuci	⊢ ( Ord 2o → Ord suc 2o )
4	1 2 3	mp2b	⊢ Ord suc 2o
5		df-3o	⊢ 3o = suc 2o
6		ordeq	⊢ ( 3o = suc 2o → ( Ord 3o ↔ Ord suc 2o ) )
7	5 6	ax-mp	⊢ ( Ord 3o ↔ Ord suc 2o )
8	4 7	mpbir	⊢ Ord 3o