Theorem snoceqd | index | src |

theorem snoceqd (_G: wff) (_l1 _l2 _a1 _a2: nat):
  $ _G -> _l1 = _l2 $ >
  $ _G -> _a1 = _a2 $ >
  $ _G -> _l1 |> _a1 = _l2 |> _a2 $;
StepHypRefExpression
1 hyp _lh
_G -> _l1 = _l2
2 hyp _ah
_G -> _a1 = _a2
3 eqidd
_G -> 0 = 0
4 2, 3 conseqd
_G -> _a1 : 0 = _a2 : 0
5 1, 4 appendeqd
_G -> _l1 ++ _a1 : 0 = _l2 ++ _a2 : 0
6 5 conv snoc
_G -> _l1 |> _a1 = _l2 |> _a2

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)