Theorem eluzfz2

Description: Membership in a finite set of sequential integers - special case. (Contributed by NM, 13-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

	Ref	Expression
Assertion	eluzfz2	|- ( N e. ( ZZ>= ` M ) -> N e. ( M ... N ) )

Proof

Step	Hyp	Ref	Expression
1		eluzelz	|- ( N e. ( ZZ>= ` M ) -> N e. ZZ )
2		uzid	|- ( N e. ZZ -> N e. ( ZZ>= ` N ) )
3	1 2	syl	|- ( N e. ( ZZ>= ` M ) -> N e. ( ZZ>= ` N ) )
4		eluzfz	|- ( ( N e. ( ZZ>= ` M ) /\ N e. ( ZZ>= ` N ) ) -> N e. ( M ... N ) )
5	3 4	mpdan	|- ( N e. ( ZZ>= ` M ) -> N e. ( M ... N ) )