Theorem uzidd

Description: Membership of the least member in an upper set of integers. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	uzidd.1	⊢ ( 𝜑 → 𝑀 ∈ ℤ )
Assertion	uzidd	⊢ ( 𝜑 → 𝑀 ∈ ( ℤ≥ ‘ 𝑀 ) )

Proof

Step	Hyp	Ref	Expression
1		uzidd.1	⊢ ( 𝜑 → 𝑀 ∈ ℤ )
2		uzid	⊢ ( 𝑀 ∈ ℤ → 𝑀 ∈ ( ℤ≥ ‘ 𝑀 ) )
3	1 2	syl	⊢ ( 𝜑 → 𝑀 ∈ ( ℤ≥ ‘ 𝑀 ) )