theorem sappapp (F: set) (a b: nat): $ F @@ a @ b = F @ (a, b) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
theeq |
{a1 | b, a1 e. F @@ a} == {a2 | (a, b), a2 e. F} -> the {a1 | b, a1 e. F @@ a} = the {a2 | (a, b), a2 e. F} |
| 2 |
1 |
conv app |
{a1 | b, a1 e. F @@ a} == {a2 | (a, b), a2 e. F} -> F @@ a @ b = F @ (a, b) |
| 3 |
|
sapprapp |
F @@ a @' b == F @' (a, b) |
| 4 |
3 |
conv rapp |
{a1 | b, a1 e. F @@ a} == {a2 | (a, b), a2 e. F} |
| 5 |
2, 4 |
ax_mp |
F @@ a @ b = F @ (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,
the0),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)