theorem maxeqd (_G: wff) (_a1 _a2 _b1 _b2: nat):
$ _G -> _a1 = _a2 $ >
$ _G -> _b1 = _b2 $ >
$ _G -> max _a1 _b1 = max _a2 _b2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _ah |
_G -> _a1 = _a2 |
| 2 |
|
hyp _bh |
_G -> _b1 = _b2 |
| 3 |
1, 2 |
lteqd |
_G -> (_a1 < _b1 <-> _a2 < _b2) |
| 4 |
3, 2, 1 |
ifeqd |
_G -> if (_a1 < _b1) _b1 _a1 = if (_a2 < _b2) _b2 _a2 |
| 5 |
4 |
conv max |
_G -> max _a1 _b1 = max _a2 _b2 |
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)