Theorem lmemeq2d ≪ | index | src | ≫

theorem lmemeq2d (_G: wff) (a _l1 _l2: nat):
  $ _G -> _l1 = _l2 $ >
  $ _G -> (a IN _l1 <-> a IN _l2) $;

Step	Hyp	Ref	Expression
1		eqidd	_G -> a = a
2		hyp _h	_G -> _l1 = _l2
3	1, 2	lmemeqd	_G -> (a IN _l1 <-> a IN _l2)

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 (peano2, addeq, muleq)