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 |
2 |
muleq1d |
_G -> _a1 * b = _a2 * b |
| 4 |
|
eqidd |
_G -> 1 = 1 |
| 5 |
1, 3, 4 |
eqmeqd |
_G -> (mod(_n1): _a1 * b = 1 <-> mod(_n2): _a2 * b = 1) |
| 6 |
5 |
abeqd |
_G -> {b | mod(_n1): _a1 * b = 1} == {b | mod(_n2): _a2 * b = 1} |
| 7 |
6 |
leasteqd |
_G -> least {b | mod(_n1): _a1 * b = 1} = least {b | mod(_n2): _a2 * b = 1} |
| 8 |
7 |
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)