Theorem zsubeqd | index | src |

theorem zsubeqd (_G: wff) (_m1 _m2 _n1 _n2: nat):
  $ _G -> _m1 = _m2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> _m1 -Z _n1 = _m2 -Z _n2 $;
StepHypRefExpression
1 hyp _mh
_G -> _m1 = _m2
2 hyp _nh
_G -> _n1 = _n2
3 2 znegeqd
_G -> -uZ _n1 = -uZ _n2
4 1, 3 zaddeqd
_G -> _m1 +Z -uZ _n1 = _m2 +Z -uZ _n2
5 4 conv zsub
_G -> _m1 -Z _n1 = _m2 -Z _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, muleq)