theorem eqm11 (a b: nat): $ mod(1): a = b $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqtr4 |
a % 1 = 0 -> b % 1 = 0 -> a % 1 = b % 1 |
| 2 |
1 |
conv eqm |
a % 1 = 0 -> b % 1 = 0 -> mod(1): a = b |
| 3 |
|
mod12 |
a % 1 = 0 |
| 4 |
2, 3 |
ax_mp |
b % 1 = 0 -> mod(1): a = b |
| 5 |
|
mod12 |
b % 1 = 0 |
| 6 |
4, 5 |
ax_mp |
mod(1): a = b |
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),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)