Theorem lmemconsid ≪ | index | src | ≫

theorem lmemconsid (a l: nat): $ a IN a : l $;

Step	Hyp	Ref	Expression
1		lmemS	a IN a : l <-> a = a \/ a IN l
2		orl	a = a -> a = a \/ a IN l
3		eqid	a = a
4	2, 3	ax_mp	a = a \/ a IN l
5	1, 4	mpbir	a IN a : l

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)