Theorem el01 ≪ | index | src | ≫

theorem el01 (a: nat): $ 0 e. a <-> odd a $;

Step	Hyp	Ref	Expression
1		bitr	(0 e. a <-> odd (shr a 0)) -> (odd (shr a 0) <-> odd a) -> (0 e. a <-> odd a)
2		elnel	0 e. a <-> odd (shr a 0)
3	1, 2	ax_mp	(odd (shr a 0) <-> odd a) -> (0 e. a <-> odd a)
4		oddeq	shr a 0 = a -> (odd (shr a 0) <-> odd a)
5		shr02	shr a 0 = a
6	4, 5	ax_mp	odd (shr a 0) <-> odd a
7	3, 6	ax_mp	0 e. a <-> odd 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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)