Metamath Proof Explorer


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* )