Metamath Proof Explorer


Theorem fzelp1

Description: Membership in a set of sequential integers with an appended element. (Contributed by NM, 7-Dec-2005) (Revised by Mario Carneiro, 28-Apr-2015)

Ref Expression
Assertion fzelp1
|- ( K e. ( M ... N ) -> K e. ( M ... ( N + 1 ) ) )

Proof

Step Hyp Ref Expression
1 fzssp1
 |-  ( M ... N ) C_ ( M ... ( N + 1 ) )
2 1 sseli
 |-  ( K e. ( M ... N ) -> K e. ( M ... ( N + 1 ) ) )