Theorem ntheq | index | src |

theorem ntheq (_n1 _n2 _l1 _l2: nat):
  $ _n1 = _n2 -> _l1 = _l2 -> nth _n1 _l1 = nth _n2 _l2 $;
StepHypRefExpression
1 anl
_n1 = _n2 /\ _l1 = _l2 -> _n1 = _n2
2 anr
_n1 = _n2 /\ _l1 = _l2 -> _l1 = _l2
3 1, 2 ntheqd
_n1 = _n2 /\ _l1 = _l2 -> nth _n1 _l1 = nth _n2 _l2
4 3 exp
_n1 = _n2 -> _l1 = _l2 -> nth _n1 _l1 = nth _n2 _l2

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)