theorem zabseqd (_G: wff) (_n1 _n2: nat):
$ _G -> _n1 = _n2 $ >
$ _G -> zabs _n1 = zabs _n2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _nh |
_G -> _n1 = _n2 |
| 2 |
1 |
zfsteqd |
_G -> zfst _n1 = zfst _n2 |
| 3 |
1 |
zsndeqd |
_G -> zsnd _n1 = zsnd _n2 |
| 4 |
2, 3 |
addeqd |
_G -> zfst _n1 + zsnd _n1 = zfst _n2 + zsnd _n2 |
| 5 |
4 |
conv zabs |
_G -> zabs _n1 = zabs _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)