This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem elfz3

Description: Membership in a finite set of sequential integers containing one integer. (Contributed by NM, 21-Jul-2005)

Ref Expression
Assertion elfz3 
|- ( N e. ZZ -> N e. ( N ... N ) )

Proof

Step Hyp Ref Expression
1 uzid 
 |-  ( N e. ZZ -> N e. ( ZZ>= ` N ) )
2 eluzfz1 
 |-  ( N e. ( ZZ>= ` N ) -> N e. ( N ... N ) )
3 1 2 syl 
 |-  ( N e. ZZ -> N e. ( N ... N ) )