Theorem Tail_ocasep ≪ | index | src | ≫

theorem Tail_ocasep (S: set) (z: wff): $ Tail (ocasep z S) == S $;

Step	Hyp	Ref	Expression
1		bitr	(a1 e. Tail (ocasep z S) <-> suc a1 e. ocasep z S) -> (suc a1 e. ocasep z S <-> a1 e. S) -> (a1 e. Tail (ocasep z S) <-> a1 e. S)
2		elTail	a1 e. Tail (ocasep z S) <-> suc a1 e. ocasep z S
3	1, 2	ax_mp	(suc a1 e. ocasep z S <-> a1 e. S) -> (a1 e. Tail (ocasep z S) <-> a1 e. S)
4		ocasepS	suc a1 e. ocasep z S <-> a1 e. S
5	3, 4	ax_mp	a1 e. Tail (ocasep z S) <-> a1 e. S
6	5	ax_gen	A. a1 (a1 e. Tail (ocasep z S) <-> a1 e. S)
7	6	conv eqs	Tail (ocasep z S) == S

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 (peano1, peano2, peano5, addeq, add0, addS)