Theorem eqin2 ≪ | index | src | ≫

theorem eqin2 (A B: set): $ A C_ B <-> B i^i A == A $;

Step	Hyp	Ref	Expression
1		bitr	(A C_ B <-> A i^i B == A) -> (A i^i B == A <-> B i^i A == A) -> (A C_ B <-> B i^i A == A)
2		eqin1	A C_ B <-> A i^i B == A
3	1, 2	ax_mp	(A i^i B == A <-> B i^i A == A) -> (A C_ B <-> B i^i A == A)
4		eqseq1	A i^i B == B i^i A -> (A i^i B == A <-> B i^i A == A)
5		incom	A i^i B == B i^i A
6	4, 5	ax_mp	A i^i B == A <-> B i^i A == A
7	3, 6	ax_mp	A C_ B <-> B 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)