theorem sublistAteq2d (_G: wff) (n _L11 _L12 L2: nat):
$ _G -> _L11 = _L12 $ >
$ _G -> (sublistAt n _L11 L2 <-> sublistAt n _L12 L2) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqidd |
_G -> n = n |
| 2 |
|
hyp _h |
_G -> _L11 = _L12 |
| 3 |
|
eqidd |
_G -> L2 = L2 |
| 4 |
1, 2, 3 |
sublistAteqd |
_G -> (sublistAt n _L11 L2 <-> sublistAt n _L12 L2) |
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)