Theorem ocasep0 ≪ | index | src | ≫

theorem ocasep0 (S: set) (z: wff): $ 0 e. ocasep z S <-> z $;

Step	Hyp	Ref	Expression
1		ifppos	a1 = 0 -> (ifp (a1 = 0) z (a1 - 1 e. S) <-> z)
2	1	elabe	0 e. {a1 \| ifp (a1 = 0) z (a1 - 1 e. S)} <-> z
3	2	conv ocasep	0 e. ocasep z S <-> z

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)