Theorem inss1 ≪ | index | src | ≫

theorem inss1 (A B: set): $ A i^i B C_ A $;

Step	Hyp	Ref	Expression
1		elin	x e. A i^i B <-> x e. A /\ x e. B
2		anl	x e. A /\ x e. B -> x e. A
3	1, 2	sylbi	x e. A i^i B -> x e. A
4	3	ax_gen	A. x (x e. A i^i B -> x e. A)
5	4	conv subset	A i^i B C_ 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)