Theorem sucne0 ≪ | index | src | ≫ 

theorem sucne0 (a b: nat): $ a = suc b -> a != 0 $;
StepHypRefExpression
1 peano1 
suc b != 0
2 neeq1 
a = suc b -> (a != 0 <-> suc b != 0)
3 1, 2 mpbiri 
a = suc b -> a != 0

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7), axs_peano (peano1)