Theorem lmemsnocid | index | src |

theorem lmemsnocid (a l: nat): $ a IN l |> a $;
StepHypRefExpression
1 lmemsnoc
a IN l |> a <-> a IN l \/ a = a
2 orr
a = a -> a IN l \/ a = a
3 eqid
a = a
4 2, 3 ax_mp
a IN l \/ a = a
5 1, 4 mpbir
a IN l |> a

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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)