Theorem uzxrd

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

	Ref	Expression
Hypotheses	uzxrd.1	⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
	uzxrd.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑍 )
Assertion	uzxrd	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )

Proof

Step	Hyp	Ref	Expression
1		uzxrd.1	⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
2		uzxrd.2	⊢ ( 𝜑 → 𝐴 ∈ 𝑍 )
3		ressxr	⊢ ℝ ⊆ ℝ*
4	1 2	uzred	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
5	3 4	sseldi	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )