theorem all202 (R: set) (l: nat): $ l, 0 e. all2 R <-> l = 0 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bitr3 |
(0, l e. all2 (cnv R) <-> l, 0 e. all2 R) -> (0, l e. all2 (cnv R) <-> l = 0) -> (l, 0 e. all2 R <-> l = 0) |
| 2 |
|
all2com |
0, l e. all2 (cnv R) <-> l, 0 e. all2 R |
| 3 |
1, 2 |
ax_mp |
(0, l e. all2 (cnv R) <-> l = 0) -> (l, 0 e. all2 R <-> l = 0) |
| 4 |
|
all201 |
0, l e. all2 (cnv R) <-> l = 0 |
| 5 |
3, 4 |
ax_mp |
l, 0 e. all2 R <-> l = 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)