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 ∈ ( 𝑀 ... 𝑁 ) → 𝐾 ∈ ( 𝑀 ... ( 𝑁 + 1 ) ) )

Proof

Step Hyp Ref Expression
1 fzssp1 ( 𝑀 ... 𝑁 ) ⊆ ( 𝑀 ... ( 𝑁 + 1 ) )
2 1 sseli ( 𝐾 ∈ ( 𝑀 ... 𝑁 ) → 𝐾 ∈ ( 𝑀 ... ( 𝑁 + 1 ) ) )