theorem xppi12 (A B C: set) (a: nat): $ a e. Xp (Xp A B) C -> pi12 a e. B $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
xpfst |
a e. Xp (Xp A B) C -> fst a e. Xp A B |
| 2 |
|
xpsnd |
fst a e. Xp A B -> snd (fst a) e. B |
| 3 |
2 |
conv pi12 |
fst a e. Xp A B -> pi12 a e. B |
| 4 |
1, 3 |
rsyl |
a e. Xp (Xp A B) C -> pi12 a e. 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)