Theorem recnd

Description: Deduction from real number to complex number. (Contributed by NM, 26-Oct-1999)

	Ref	Expression
Hypothesis	recnd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	recnd	⊢ ( 𝜑 → 𝐴 ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		recnd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		recn	⊢ ( 𝐴 ∈ ℝ → 𝐴 ∈ ℂ )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ∈ ℂ )