Theorem remulcli

Description: Closure law for multiplication of reals. (Contributed by NM, 17-Jan-1997)

	Ref	Expression
Hypotheses	recni.1	⊢ 𝐴 ∈ ℝ
	axri.2	⊢ 𝐵 ∈ ℝ
Assertion	remulcli	⊢ ( 𝐴 · 𝐵 ) ∈ ℝ

Proof

Step	Hyp	Ref	Expression
1		recni.1	⊢ 𝐴 ∈ ℝ
2		axri.2	⊢ 𝐵 ∈ ℝ
3		remulcl	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ) → ( 𝐴 · 𝐵 ) ∈ ℝ )
4	1 2 3	mp2an	⊢ ( 𝐴 · 𝐵 ) ∈ ℝ