Theorem invmeqd ≪ | index | src | ≫

theorem invmeqd (_G: wff) (_a1 _a2 _n1 _n2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> invm _a1 _n1 = invm _a2 _n2 $;

Step	Hyp	Ref	Expression
1		hyp _nh	_G -> _n1 = _n2
2		hyp _ah	_G -> _a1 = _a2
3		eqidd	_G -> b = b
4	2, 3	muleqd	_G -> _a1 * b = _a2 * b
5		eqidd	_G -> 1 = 1
6	1, 4, 5	eqmeqd	_G -> (mod(_n1): _a1 * b = 1 <-> mod(_n2): _a2 * b = 1)
7	6	abeqd	_G -> {b \| mod(_n1): _a1 * b = 1} == {b \| mod(_n2): _a2 * b = 1}
8	7	leasteqd	_G -> least {b \| mod(_n1): _a1 * b = 1} = least {b \| mod(_n2): _a2 * b = 1}
9	8	conv invm	_G -> invm _a1 _n1 = invm _a2 _n2

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 (peano2, addeq, muleq)