Theorem znsubeq2d ≪ | index | src | ≫ 

theorem znsubeq2d (_G: wff) (m _n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> m -ZN _n1 = m -ZN _n2 $;
StepHypRefExpression
1 eqidd 
_G -> m = m
2 hyp _h 
_G -> _n1 = _n2
3 1, 2 znsubeqd 
_G -> m -ZN _n1 = m -ZN _n2

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano2, addeq)