theorem SndSum (A B: set): $ Snd (Sum A B) == B $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
bitr |
(a1 e. Snd (Sum A B) <-> b1 a1 e. Sum A B) -> (b1 a1 e. Sum A B <-> a1 e. B) -> (a1 e. Snd (Sum A B) <-> a1 e. B) |
| 2 |
|
elSnd |
a1 e. Snd (Sum A B) <-> b1 a1 e. Sum A B |
| 3 |
1, 2 |
ax_mp |
(b1 a1 e. Sum A B <-> a1 e. B) -> (a1 e. Snd (Sum A B) <-> a1 e. B) |
| 4 |
|
Sumr |
b1 a1 e. Sum A B <-> a1 e. B |
| 5 |
3, 4 |
ax_mp |
a1 e. Snd (Sum A B) <-> a1 e. B |
| 6 |
5 |
ax_gen |
A. a1 (a1 e. Snd (Sum A B) <-> a1 e. B) |
| 7 |
6 |
conv eqs |
Snd (Sum A B) == 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,
the0),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)