Theorem rpred

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

	Ref	Expression
Hypothesis	rpred.1	$$⊢\phi \to A\in {ℝ}^{+}$$
Assertion	rpred	$$⊢\phi \to A\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		rpred.1	$$⊢\phi \to A\in {ℝ}^{+}$$
2		rpssre	$$⊢{ℝ}^{+}\subseteq ℝ$$
3	2 1	sseldi	$$⊢\phi \to A\in ℝ$$