theorem odd0: $ ~odd 0 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqeq1 |
0 % 2 = 0 -> (0 % 2 = 1 <-> 0 = 1) |
| 2 |
1 |
conv odd |
0 % 2 = 0 -> (odd 0 <-> 0 = 1) |
| 3 |
|
mod01 |
0 % 2 = 0 |
| 4 |
2, 3 |
ax_mp |
odd 0 <-> 0 = 1 |
| 5 |
|
eqcom |
0 = 1 -> 1 = 0 |
| 6 |
|
d1ne0 |
1 != 0 |
| 7 |
6 |
conv ne |
~1 = 0 |
| 8 |
5, 7 |
mt |
~0 = 1 |
| 9 |
4, 8 |
mtbir |
~odd 0 |
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
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)