theorem shleqd (_G: wff) (_a1 _a2 _n1 _n2: nat):
$ _G -> _a1 = _a2 $ >
$ _G -> _n1 = _n2 $ >
$ _G -> shl _a1 _n1 = shl _a2 _n2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _ah |
_G -> _a1 = _a2 |
| 2 |
|
eqidd |
_G -> 2 = 2 |
| 3 |
|
hyp _nh |
_G -> _n1 = _n2 |
| 4 |
2, 3 |
poweqd |
_G -> 2 ^ _n1 = 2 ^ _n2 |
| 5 |
1, 4 |
muleqd |
_G -> _a1 * 2 ^ _n1 = _a2 * 2 ^ _n2 |
| 6 |
5 |
conv shl |
_G -> shl _a1 _n1 = shl _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)