Description: Closure law for division of reals. (Contributed by NM, 9-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | redivcl.1 | ⊢ 𝐴 ∈ ℝ | |
redivcl.2 | ⊢ 𝐵 ∈ ℝ | ||
Assertion | redivclzi | ⊢ ( 𝐵 ≠ 0 → ( 𝐴 / 𝐵 ) ∈ ℝ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | redivcl.1 | ⊢ 𝐴 ∈ ℝ | |
2 | redivcl.2 | ⊢ 𝐵 ∈ ℝ | |
3 | redivcl | ⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ∧ 𝐵 ≠ 0 ) → ( 𝐴 / 𝐵 ) ∈ ℝ ) | |
4 | 1 2 3 | mp3an12 | ⊢ ( 𝐵 ≠ 0 → ( 𝐴 / 𝐵 ) ∈ ℝ ) |