Theorem axlowdimlem2

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

	Ref	Expression
Assertion	axlowdimlem2	⊢ ( ( 1 ... 2 ) ∩ ( 3 ... 𝑁 ) ) = ∅

Proof

Step	Hyp	Ref	Expression
1		2lt3	⊢ 2 < 3
2		fzdisj	⊢ ( 2 < 3 → ( ( 1 ... 2 ) ∩ ( 3 ... 𝑁 ) ) = ∅ )
3	1 2	ax-mp	⊢ ( ( 1 ... 2 ) ∩ ( 3 ... 𝑁 ) ) = ∅