Theorem qred

Description: A rational number is a real number. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	qred.1	⊢ ( 𝜑 → 𝐴 ∈ ℚ )
Assertion	qred	⊢ ( 𝜑 → 𝐴 ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		qred.1	⊢ ( 𝜑 → 𝐴 ∈ ℚ )
2		qre	⊢ ( 𝐴 ∈ ℚ → 𝐴 ∈ ℝ )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ∈ ℝ )