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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 ) ) )