Theorem conscan2 ≪ | index | src | ≫

theorem conscan2 (a b c: nat): $ a : b = a : c <-> b = c $;

Step	Hyp	Ref	Expression
1		bitr	(a : b = a : c <-> a = a /\ b = c) -> (a = a /\ b = c <-> b = c) -> (a : b = a : c <-> b = c)
2		consinj	a : b = a : c <-> a = a /\ b = c
3	1, 2	ax_mp	(a = a /\ b = c <-> b = c) -> (a : b = a : c <-> b = c)
4		bian1	a = a -> (a = a /\ b = c <-> b = c)
5		eqid	a = a
6	4, 5	ax_mp	a = a /\ b = c <-> b = c
7	3, 6	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)