Theorem rreci_closed

Theorem. rreci_closed
a ∈ ℝ → ¬a = 0 → 1/a ∈ ℝ
Proof
01. 1 ⊢ a ∈ ℝ, hypo.
02. 2 ⊢ ¬a = 0, hypo.
03. ⊢ 1 ∈ ℝ, calc.
04. 1, 2 ⊢ 1/a ∈ ℝ, rdiv_closed 3 1 2.
rreci_closed. ⊢ a ∈ ℝ → ¬a = 0 → 1/a ∈ ℝ,
  subj_intro_ii 4.

Dependencies
The given proof depends on four axioms:
eq_refl, eq_subst, rinv_closed, rmul_closed.