Theorem ltpr2 ≪ | index | src | ≫

theorem ltpr2 (a b c: nat): $ b < c <-> a, b < a, c $;

Step	Hyp	Ref	Expression
1		ltnle	b < c <-> ~c <= b
2		ltnle	a, b < a, c <-> ~a, c <= a, b
3		noteq	(c <= b <-> a, c <= a, b) -> (~c <= b <-> ~a, c <= a, b)
4		lepr2	c <= b <-> a, c <= a, b
5	3, 4	ax_mp	~c <= b <-> ~a, c <= a, b
6	1, 2, 5	bitr4gi	b < c <-> a, b < a, c

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)