theorem obindeqd (_G: wff) (_a1 _a2: nat) (_F1 _F2: set):
$ _G -> _a1 = _a2 $ >
$ _G -> _F1 == _F2 $ >
$ _G -> obind _a1 _F1 = obind _a2 _F2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqidd |
_G -> 0 = 0 |
| 2 |
|
hyp _Fh |
_G -> _F1 == _F2 |
| 3 |
1, 2 |
ocaseeqd |
_G -> ocase 0 _F1 == ocase 0 _F2 |
| 4 |
|
hyp _ah |
_G -> _a1 = _a2 |
| 5 |
3, 4 |
appeqd |
_G -> ocase 0 _F1 @ _a1 = ocase 0 _F2 @ _a2 |
| 6 |
5 |
conv obind |
_G -> obind _a1 _F1 = obind _a2 _F2 |
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)