Theorem incpl1 ≪ | index | src | ≫

theorem incpl1 (A: set): $ Compl A i^i A == 0 $;

Step	Hyp	Ref	Expression
1		eqstr	Compl A i^i A == A i^i Compl A -> A i^i Compl A == 0 -> Compl A i^i A == 0
2		incom	Compl A i^i A == A i^i Compl A
3	1, 2	ax_mp	A i^i Compl A == 0 -> Compl A i^i A == 0
4		incpl2	A i^i Compl A == 0
5	3, 4	ax_mp	Compl A i^i A == 0

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, muleq, add0, addS, mul0, mulS)