Theorem Arrowdm ≪ | index | src | ≫ 

theorem Arrowdm (A B: set) (f: nat): $ f e. Arrow A B -> Dom f == A $;
StepHypRefExpression
1 elArrow 
f e. Arrow A B <-> func f A B
2 funcdm 
func f A B -> Dom f == A
3 1, 2 sylbi 
f e. Arrow A B -> Dom f == 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_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano2, addeq, muleq)