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Metamath Proof Explorer

Theorem ltrelpi

Description: Positive integer 'less than' is a relation on positive integers. (Contributed by NM, 8-Feb-1996) (New usage is discouraged.)

		Ref	Expression
	Assertion	ltrelpi	$⊢ <_{𝑵} \subseteq 𝑵 \times 𝑵$

Step	Hyp	Ref	Expression
1		df-lti	$⊢ <_{𝑵} = E \cap (𝑵 \times 𝑵)$
2		inss2	$⊢ E \cap (𝑵 \times 𝑵) \subseteq 𝑵 \times 𝑵$
3	1 2	eqsstri	$⊢ <_{𝑵} \subseteq 𝑵 \times 𝑵$