theorem ndmapp (F: set) (a: nat): $ ~a e. Dom F -> F @ a = 0 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
preldm |
a, y e. F -> a e. Dom F |
| 2 |
|
absurd |
~a e. Dom F -> a e. Dom F -> y = 0 |
| 3 |
1, 2 |
syl5 |
~a e. Dom F -> a, y e. F -> y = 0 |
| 4 |
3 |
eqthe0abd |
~a e. Dom F -> the {y | a, y e. F} = 0 |
| 5 |
4 |
conv app |
~a e. Dom F -> F @ a = 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
(peano2,
addeq,
muleq)