Theorem coprimeeq1d ≪ | index | src | ≫

theorem coprimeeq1d (_G: wff) (_a1 _a2 b: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> (coprime _a1 b <-> coprime _a2 b) $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _a1 = _a2
2		eqidd	_G -> b = b
3	1, 2	coprimeeqd	_G -> (coprime _a1 b <-> coprime _a2 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 (muleq)