Theorem rpred

Description: A positive real is a real. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion	rpred	⊢ ( 𝜑 → 𝐴 ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2		rpssre	⊢ ℝ+ ⊆ ℝ
3	2 1	sseldi	⊢ ( 𝜑 → 𝐴 ∈ ℝ )