Theorem necom ≪ | index | src | ≫ 

theorem necom (a b: nat): $ a != b -> b != a $;
StepHypRefExpression
1 con3 
(b = a -> a = b) -> ~a = b -> ~b = a
2 1 conv ne 
(b = a -> a = b) -> a != b -> b != a
3 eqcom 
b = a -> a = b
4 2, 3 ax_mp 
a != b -> b != a

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)