Theorem inv1 ≪ | index | src | ≫

theorem inv1 (A: set): $ _V i^i A == A $;

Step	Hyp	Ref	Expression
1		bitr	(x e. _V i^i A <-> x e. _V /\ x e. A) -> (x e. _V /\ x e. A <-> x e. A) -> (x e. _V i^i A <-> x e. A)
2		elin	x e. _V i^i A <-> x e. _V /\ x e. A
3	1, 2	ax_mp	(x e. _V /\ x e. A <-> x e. A) -> (x e. _V i^i A <-> x e. A)
4		bian1	x e. _V -> (x e. _V /\ x e. A <-> x e. A)
5		elv	x e. _V
6	4, 5	ax_mp	x e. _V /\ x e. A <-> x e. A
7	3, 6	ax_mp	x e. _V i^i A <-> x e. A
8	7	eqri	_V i^i A == 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)