Theorem elnel ≪ | index | src | ≫

theorem elnel (a b: nat): $ a e. b <-> odd (shr b a) $;

Step	Hyp	Ref	Expression
1		eqidd	_1 = a -> b = b
2		id	_1 = a -> _1 = a
3	1, 2	shreqd	_1 = a -> shr b _1 = shr b a
4	3	oddeqd	_1 = a -> (odd (shr b _1) <-> odd (shr b a))
5	4	elabe	a e. {_1 \| odd (shr b _1)} <-> odd (shr b a)
6	5	conv ns	a e. b <-> odd (shr b 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), axs_the (theid, the0), axs_peano (peano2, addeq, muleq)