Theorem rexrd

Description: A standard real is an extended real. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rexrd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	rexrd	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )

Proof

Step	Hyp	Ref	Expression
1		rexrd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		ressxr	⊢ ℝ ⊆ ℝ*
3	2 1	sselid	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )