theorem cbvlamd {x y: nat} (G: wff) (a: nat x) (b: nat y):
$ G /\ x = y -> a = b $ >
$ G -> \ x, a == \ y, b $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
cbvlams |
\ x, a == \ y, N[y / x] a |
| 2 |
1 |
a1i |
G -> \ x, a == \ y, N[y / x] a |
| 3 |
|
sbnet |
A. x (x = y -> a = b) -> N[y / x] a = b |
| 4 |
|
hyp h |
G /\ x = y -> a = b |
| 5 |
4 |
ialda |
G -> A. x (x = y -> a = b) |
| 6 |
3, 5 |
syl |
G -> N[y / x] a = b |
| 7 |
6 |
lameqd |
G -> \ y, N[y / x] a == \ y, b |
| 8 |
2, 7 |
eqstrd |
G -> \ x, a == \ y, 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
(peano2,
addeq,
muleq)