theorem rlameqd (_G: wff) {x: nat} (_a1 _a2 _v1 _v2: nat x):
$ _G -> _a1 = _a2 $ >
$ _G -> _v1 = _v2 $ >
$ _G -> \. x e. _a1, _v1 = \. x e. _a2, _v2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _vh |
_G -> _v1 = _v2 |
| 2 |
1 |
lameqd |
_G -> \ x, _v1 == \ x, _v2 |
| 3 |
|
hyp _ah |
_G -> _a1 = _a2 |
| 4 |
3 |
nseqd |
_G -> _a1 == _a2 |
| 5 |
2, 4 |
reseqd |
_G -> (\ x, _v1) |` _a1 == (\ x, _v2) |` _a2 |
| 6 |
5 |
lowereqd |
_G -> lower ((\ x, _v1) |` _a1) = lower ((\ x, _v2) |` _a2) |
| 7 |
6 |
conv rlam |
_G -> \. x e. _a1, _v1 = \. x e. _a2, _v2 |
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)