Theorem ltner ≪ | index | src | ≫ 

theorem ltner (a b: nat): $ a < b -> b != a $;
StepHypRefExpression
1 necom 
a != b -> b != a
2 ltne 
a < b -> a != b
3 1, 2 syl 
a < b -> b != 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_peano (peano1, peano2, peano5, addeq, add0, addS)