Theorem uzxr

Description: An upper integer is an extended real. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Assertion	uzxr	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝐴 ∈ ℝ* )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( ℤ≥ ‘ 𝑀 ) = ( ℤ≥ ‘ 𝑀 )
2		id	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝐴 ∈ ( ℤ≥ ‘ 𝑀 ) )
3	1 2	uzxrd	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 𝑀 ) → 𝐴 ∈ ℝ* )