theorem zsndeqd (_G: wff) (_n1 _n2: nat):
$ _G -> _n1 = _n2 $ >
$ _G -> zsnd _n1 = zsnd _n2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqsidd |
_G -> case (\ mpos, 0) (\ mneg, suc mneg) == case (\ mpos, 0) (\ mneg, suc mneg) |
| 2 |
|
hyp _nh |
_G -> _n1 = _n2 |
| 3 |
1, 2 |
appeqd |
_G -> case (\ mpos, 0) (\ mneg, suc mneg) @ _n1 = case (\ mpos, 0) (\ mneg, suc mneg) @ _n2 |
| 4 |
3 |
conv zsnd |
_G -> zsnd _n1 = zsnd _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)