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Metamath Proof Explorer

Theorem pion

Description: A positive integer is an ordinal number. (Contributed by NM, 23-Mar-1996) (New usage is discouraged.)

		Ref	Expression
	Assertion	pion	⊢ ( 𝐴 ∈ N → 𝐴 ∈ On )

Step	Hyp	Ref	Expression
1		pinn	⊢ ( 𝐴 ∈ N → 𝐴 ∈ ω )
2		nnon	⊢ ( 𝐴 ∈ ω → 𝐴 ∈ On )
3	1 2	syl	⊢ ( 𝐴 ∈ N → 𝐴 ∈ On )