Theorem axlowdimlem2

Description: Lemma for axlowdim . Show that two sets are disjoint. (Contributed by Scott Fenton, 29-Jun-2013)

	Ref	Expression
Assertion	axlowdimlem2	$$⊢\left(1\dots 2\right)\cap \left(3\dots N\right)=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		2lt3	$$⊢2<3$$
2		fzdisj	$$⊢2<3\to \left(1\dots 2\right)\cap \left(3\dots N\right)=\varnothing$$
3	1 2	ax-mp	$$⊢\left(1\dots 2\right)\cap \left(3\dots N\right)=\varnothing$$