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	$$⊢K\in \left(M\dots N\right)\to K\in \left(M\dots N+1\right)$$

Proof

Step	Hyp	Ref	Expression
1		fzssp1	$$⊢\left(M\dots N\right)\subseteq \left(M\dots N+1\right)$$
2	1	sseli	$$⊢K\in \left(M\dots N\right)\to K\in \left(M\dots N+1\right)$$