Theorem lecons1 ≪ | index | src | ≫

theorem lecons1 (a b c: nat): $ a <= b <-> a : c <= b : c $;

Step	Hyp	Ref	Expression
1		bitr	(a <= b <-> a, c <= b, c) -> (a, c <= b, c <-> a : c <= b : c) -> (a <= b <-> a : c <= b : c)
2		lepr1	a <= b <-> a, c <= b, c
3	1, 2	ax_mp	(a, c <= b, c <-> a : c <= b : c) -> (a <= b <-> a : c <= b : c)
4		lesuc	a, c <= b, c <-> suc (a, c) <= suc (b, c)
5	4	conv cons	a, c <= b, c <-> a : c <= b : c
6	3, 5	ax_mp	a <= b <-> a : c <= b : 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)