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Metamath Proof Explorer

Theorem 6lt8

Description: 6 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

		Ref	Expression
	Assertion	6lt8	$⊢ 6 < 8$

Step	Hyp	Ref	Expression
1		6lt7	$⊢ 6 < 7$
2		7lt8	$⊢ 7 < 8$
3		6re	$⊢ 6 \in ℝ$
4		7re	$⊢ 7 \in ℝ$
5		8re	$⊢ 8 \in ℝ$
6	3 4 5	lttri	$⊢ (6 < 7 \land 7 < 8) \to 6 < 8$
7	1 2 6	mp2an	$⊢ 6 < 8$