Theorem pow22 ≪ | index | src | ≫

theorem pow22 (a: nat): $ a ^ 2 = a * a $;

Step	Hyp	Ref	Expression
1		eqtr	a ^ 2 = a * a ^ 1 -> a * a ^ 1 = a * a -> a ^ 2 = a * a
2		powS	a ^ suc 1 = a * a ^ 1
3	2	conv d2	a ^ 2 = a * a ^ 1
4	1, 3	ax_mp	a * a ^ 1 = a * a -> a ^ 2 = a * a
5		muleq2	a ^ 1 = a -> a * a ^ 1 = a * a
6		pow12	a ^ 1 = a
7	5, 6	ax_mp	a * a ^ 1 = a * a
8	4, 7	ax_mp	a ^ 2 = 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_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)