theorem lameqd (_G: wff) {x: nat} (_a1 _a2: nat x):
$ _G -> _a1 = _a2 $ >
$ _G -> \ x, _a1 == \ x, _a2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqidd |
_G -> p = p |
| 2 |
|
eqidd |
_G -> x = x |
| 3 |
|
hyp _ah |
_G -> _a1 = _a2 |
| 4 |
2, 3 |
preqd |
_G -> x, _a1 = x, _a2 |
| 5 |
1, 4 |
eqeqd |
_G -> (p = x, _a1 <-> p = x, _a2) |
| 6 |
5 |
exeqd |
_G -> (E. x p = x, _a1 <-> E. x p = x, _a2) |
| 7 |
6 |
abeqd |
_G -> {p | E. x p = x, _a1} == {p | E. x p = x, _a2} |
| 8 |
7 |
conv lam |
_G -> \ x, _a1 == \ x, _a2 |
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)