Theorem elList ≪ | index | src | ≫ 

theorem elList (A: set) (l: nat): $ l e. List A <-> all A l $;
StepHypRefExpression
1 alleq2 
n = l -> (all A n <-> all A l)
2 1 elabe 
l e. {n | all A n} <-> all A l
3 2 conv List 
l e. List A <-> all A l

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 (peano2, addeq, muleq)