Theorem gcd02 ≪ | index | src | ≫

theorem gcd02 (a: nat): $ gcd a 0 = a $;

Step	Hyp	Ref	Expression
1		eqtr	gcd a 0 = gcd 0 a -> gcd 0 a = a -> gcd a 0 = a
2		gcdcom	gcd a 0 = gcd 0 a
3	1, 2	ax_mp	gcd 0 a = a -> gcd a 0 = a
4		gcd01	gcd 0 a = a
5	3, 4	ax_mp	gcd a 0 = 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)