Theorem mdmcan2 ≪ | index | src | ≫

theorem mdmcan2 (a b c: nat): $ c != 0 -> a * c // (b * c) = a // b $;

Step	Hyp	Ref	Expression
1		diveq	a * c = c * a -> b * c = c * b -> a * c // (b * c) = c * a // (c * b)
2		mulcom	a * c = c * a
3	1, 2	ax_mp	b * c = c * b -> a * c // (b * c) = c * a // (c * b)
4		mulcom	b * c = c * b
5	3, 4	ax_mp	a * c // (b * c) = c * a // (c * b)
6		mdmcan1	c != 0 -> c * a // (c * b) = a // b
7	5, 6	syl5eq	c != 0 -> a * c // (b * c) = 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)