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Metamath Proof Explorer

Theorem 4pos

Description: The number 4 is positive. (Contributed by NM, 27-May-1999)

		Ref	Expression
	Assertion	4pos	$⊢ 0 < 4$

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