Theorem mul21 ≪ | index | src | ≫

theorem mul21 (a: nat): $ 2 * a = a + a $;

Step	Hyp	Ref	Expression
1		eqtr	2 * a = a * 2 -> a * 2 = a + a -> 2 * a = a + a
2		mulcom	2 * a = a * 2
3	1, 2	ax_mp	a * 2 = a + a -> 2 * a = a + a
4		mul22	a * 2 = a + a
5	3, 4	ax_mp	2 * a = a + a

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_peano (peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)