Theorem ltnei | index | src |

theorem ltnei (a b: nat): $ a < b $ > $ a != b $;
StepHypRefExpression
1 ltne
a < b -> a != b
2 hyp h
a < b
3 1, 2 ax_mp
a != b

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_peano (peano1, peano2, peano5, addeq, add0, addS)