theorem sublistAteq3d (_G: wff) (n L1 _L21 _L22: nat):
$ _G -> _L21 = _L22 $ >
$ _G -> (sublistAt n L1 _L21 <-> sublistAt n L1 _L22) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqidd |
_G -> n = n |
| 2 |
|
eqidd |
_G -> L1 = L1 |
| 3 |
|
hyp _h |
_G -> _L21 = _L22 |
| 4 |
1, 2, 3 |
sublistAteqd |
_G -> (sublistAt n L1 _L21 <-> sublistAt n L1 _L22) |
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)