Theorem cong_refl

Theorem. cong_refl
a ∈ ℤ → m ∈ ℤ → cong a a m
Proof
01. 1 ⊢ a ∈ ℤ, hypo.
02. 2 ⊢ m ∈ ℤ, hypo.
03. 1 ⊢ a - a = 0, isub_self 1.
04. ⊢ 0 ∈ ℤ, calc.
05. 2 ⊢ m⋅0 = 0, imul_rzero 2.
06. 1, 2 ⊢ a - a = m⋅0, eq_trans_rr 3 5.
07. 1, 2 ⊢ cong a a m, cong_intro 4 6.
cong_refl. ⊢ a ∈ ℤ → m ∈ ℤ → cong a a m, subj_intro_ii 7.

Dependencies
The given proof depends on 11 axioms:
comp, eq_refl, eq_subst, radd_assoc, radd_closed, radd_comm, radd_inv, radd_neutr, rmul_closed, rmul_distl_add, rneg_closed.