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Metamath Proof Explorer

Theorem 3pos

Description: The number 3 is positive. (Contributed by NM, 27-May-1999)

		Ref	Expression
	Assertion	3pos	$⊢ 0 < 3$

Step	Hyp	Ref	Expression
1		2re	$⊢ 2 \in ℝ$
2		1re	$⊢ 1 \in ℝ$
3		2pos	$⊢ 0 < 2$
4		0lt1	$⊢ 0 < 1$
5	1 2 3 4	addgt0ii	$⊢ 0 < 2 + 1$
6		df-3	$⊢ 3 = 2 + 1$
7	5 6	breqtrri	$⊢ 0 < 3$