Theorem dfodd2 ≪ | index | src | ≫

theorem dfodd2 (n: nat): $ odd n <-> true (n % 2) $;

Step	Hyp	Ref	Expression
1		bicom	(true (n % 2) <-> odd n) -> (odd n <-> true (n % 2))
2		dftrue2	bool (n % 2) -> (true (n % 2) <-> n % 2 = 1)
3	2	conv odd	bool (n % 2) -> (true (n % 2) <-> odd n)
4		boolmod2	bool (n % 2)
5	3, 4	ax_mp	true (n % 2) <-> odd n
6	1, 5	ax_mp	odd n <-> true (n % 2)

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), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)