Theorem nmul_distr_add

Theorem. nmul_distr_add
a ∈ ℕ → b ∈ ℕ → c ∈ ℕ → (a + b)⋅c = a⋅c + b⋅c
Proof
nmul_distr_add. ⊢ a ∈ ℕ → b ∈ ℕ → c ∈ ℕ → (a + b)⋅c = a⋅c + b⋅c,
  pred_iii_restr nat_incl_in_real rmul_distr_add.

Dependencies
The given proof depends on seven axioms:
comp, eq_refl, eq_subst, radd_closed, real_is_set, rmul_comm, rmul_distl_add.