Theorem copcom ≪ | index | src | ≫

theorem copcom (a b: nat): $ coprime a b <-> coprime b a $;

Step	Hyp	Ref	Expression
1		eqeq1	gcd a b = gcd b a -> (gcd a b = 1 <-> gcd b a = 1)
2	1	conv coprime	gcd a b = gcd b a -> (coprime a b <-> coprime b a)
3		gcdcom	gcd a b = gcd b a
4	2, 3	ax_mp	coprime a b <-> coprime b 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 (muleq)