Theorem modeqd | index | src |

theorem modeqd (_G: wff) (_a1 _a2 _b1 _b2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> _b1 = _b2 $ >
  $ _G -> _a1 % _b1 = _a2 % _b2 $;
StepHypRefExpression
1 hyp _ah
_G -> _a1 = _a2
2 hyp _bh
_G -> _b1 = _b2
3 1, 2 diveqd
_G -> _a1 // _b1 = _a2 // _b2
4 2, 3 muleqd
_G -> _b1 * (_a1 // _b1) = _b2 * (_a2 // _b2)
5 1, 4 subeqd
_G -> _a1 - _b1 * (_a1 // _b1) = _a2 - _b2 * (_a2 // _b2)
6 5 conv mod
_G -> _a1 % _b1 = _a2 % _b2

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)