Theorem b1can ≪ | index | src | ≫

theorem b1can (a b: nat): $ b1 a = b1 b <-> a = b $;

Step	Hyp	Ref	Expression
1		eqeq	b1 a // 2 = a -> b1 b // 2 = b -> (b1 a // 2 = b1 b // 2 <-> a = b)
2		b1div2	b1 a // 2 = a
3	1, 2	ax_mp	b1 b // 2 = b -> (b1 a // 2 = b1 b // 2 <-> a = b)
4		b1div2	b1 b // 2 = b
5	3, 4	ax_mp	b1 a // 2 = b1 b // 2 <-> a = b
6		diveq1	b1 a = b1 b -> b1 a // 2 = b1 b // 2
7	5, 6	sylib	b1 a = b1 b -> a = b
8		b1eq	a = b -> b1 a = b1 b
9	7, 8	ibii	b1 a = b1 b <-> a = b

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)