Theorem optns ≪ | index | src | ≫

theorem optns (n: nat): $ Option n == b1 n $;

Step	Hyp	Ref	Expression
1		bitr4	(x e. Option n <-> x = 0 \/ x - 1 e. n) -> (x e. b1 n <-> x = 0 \/ x - 1 e. n) -> (x e. Option n <-> x e. b1 n)
2		elopt	x e. Option n <-> x = 0 \/ x - 1 e. n
3	1, 2	ax_mp	(x e. b1 n <-> x = 0 \/ x - 1 e. n) -> (x e. Option n <-> x e. b1 n)
4		elb1	x e. b1 n <-> x = 0 \/ x - 1 e. n
5	3, 4	ax_mp	x e. Option n <-> x e. b1 n
6	5	ax_gen	A. x (x e. Option n <-> x e. b1 n)
7	6	conv eqs	Option n == b1 n

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)